Palindromic Quasi_Over_Squares of the form n^2+(n+X)

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Palindromic Quasi_Over_Squares of the form n^2+(n+x)
n(n+0) n(n+1) n(n+2) n(n+x) n^2+1 n^2+x n^2–x n^2+(n+1)

Introduction

Palindromic numbers are numbers which read the same from

left to right (forwards) as from the right to left (backwards)

Here are a few random examples : 7, 3113, 44611644

Quasi_Over_Square numbers are defined and calculated by this extraordinary intricate and excruciatingly complex formula.
So, this line is for experts only

base² + ( base + X )

PLAIN TEXT QUASIMOR

Palindromic Quasi_Over_Squares

Quasi_Over_Squares of the form x² + (x + 0) can only end with a 0, 2 or 6. And if it terminates in 6, it terminates in 06 or 56 only.
Alas, my palindromes may not have leading zero's! So the zero option must not be investigated.

Main source see Palindromic Pronic Numbers

2 can be followed by any number : 20, 21, 22, 23, 24, 25, 26, 27, 28 or 29

6 can only be followed by 0 or 5 : 60 or 65

Quasi_Over_Squares of the form x² + (x + 1) can only end with a 1, 3 or 7. And if it terminates in 7, it terminates in 07 or 57 only.
Even length palindromes of this form are not possible as never divisible by 11.

Main source see Palindromic Quasi-Over-Squares

1 can be followed by any number : 10, 11, 12, 13, 14, 15, 16, 17, 18 or 19

3 can be followed by any number : 30, 31, 32, 33, 34, 35, 36, 37, 38 or 39

7 can only be followed by 0 or 5 : 70 or 75

Quasi_Over_Squares of the form x² + (x + 2) can only end with a 2, 4 or 8. And if it terminates in 8, it terminates in 08 or 58 only.

2 can be followed by any number : 20, 21, 22, 23, 24, 25, 26, 27, 28 or 29

4 can be followed by any number : 40, 41, 42, 43, 44, 45, 46, 47, 48 or 49

8 can only be followed by 0 or 5 : 80 or 85

There are no palindromic Quasi_Over_Squares of type x^2 + (x+2) of lengths 8, 14, 28, 34, 38, 48, 52, 54.

Quasi_Over_Squares of the form x² + (x + 3) can only end with a 3, 5 or 9. And if it terminates in 9, it terminates in 09 or 59 only.

3 can be followed by any number : 30, 31, 32, 33, 34, 35, 36, 37, 38 or 39

5 can be followed by any number : 50, 51, 52, 53, 54, 55, 56, 57, 58 or 59

9 can only be followed by 0 or 5 : 90 or 95 { This 90... produces ever expanding Mandelbrot-like infinite palindromes }.

There are no palindromic Quasi_Over_Squares of type x^2 + (x+3) of lengths 20, 24, 28, 30, 32, 34, 36, 44, 52, 54.

Quasi_Over_Squares of the form x² + (x + 4) can only end with a 0, 4 or 6. And if it terminates in 0, it terminates in 10 or 60 only.
Alas, my palindromes may not have leading zero's! So the zero option must not be investigated.
Even length palindromes of this form are not possible as never divisible by 11.

4 can be followed by any number : 40, 41, 42, 43, 44, 45, 46, 47, 48 or 49

6 can be followed by any number : 60, 61, 62, 63, 64, 65, 66, 67, 68 or 69

There are no palindromic Quasi_Over_Squares of type x^2 + (x+4) of EVEN length.

Quasi_Over_Squares of the form x² + (x + 5) can only end with a 1, 5 or 7. And if it terminates in 1, it terminates in 11 or 61 only.

1 can only be followed by 1 or 6 : 11 or 16

5 can be followed by any number : 50, 51, 52, 53, 54, 55, 56, 57, 58 or 59

7 can be followed by any number : 70, 71, 72, 73, 74, 75, 76, 77, 78 or 79

There are no palindromic Quasi_Over_Squares of type x^2 + (x+5) of lengths 6, 10, 12, 15, 18, 26, 28, 40, 42, 48, 49, {51 up to 54}.

Quasi_Over_Squares of the form x² + (x + 6) can only end with a 2, 6 or 8. And if it terminates in 2, it terminates in 12 or 62 only.
Even length palindromes of this form are not possible as never divisible by 11.

2 can only be followed by 1 or 6 : 21 or 26

6 can be followed by any number : 60, 61, 62, 63, 64, 65, 66, 67, 68 or 69

8 can be followed by any number : 80, 81, 82, 83, 84, 85, 86, 87, 88 or 89

There are no palindromic Quasi_Over_Squares of type x^2 + (x+6) of EVEN length nor of length 31.

Quasi_Over_Squares of the form x² + (x + 7) can only end with a 3, 7 or 9. And if it terminates in 3, it terminates in 13 or 63 only.
Even length palindromes of this form are not possible as never divisible by 11.

3 can only be followed by 1 or 6 : 31 or 36

7 can be followed by any number : 70, 71, 72, 73, 74, 75, 76, 77, 78 or 79

9 can be followed by any number : 90, 91, 92, 93, 94, 95, 96, 97, 98 or 99

There are no palindromic Quasi_Over_Squares of type x^2 + (x+7) of EVEN length.

Quasi_Over_Squares of the form x² + (x + 8) can only end with a 0, 4 or 8. And if it terminates in 4, it terminates in 14 or 64 only.
Alas, my palindromes may not have leading zero's! So the zero option must not be investigated.
Even length palindromes of this form are not possible as never divisible by 11.

4 can only be followed by 1 or 6 : 41 or 46

8 can be followed by any number : 80, 81, 82, 83, 84, 85, 86, 87, 88 or 89

There are no palindromic Quasi_Over_Squares of type x^2 + (x+8) of EVEN length nor of lengths 15, 21, 25, 45, 47.

Quasi_Over_Squares of the form x² + (x + 9) can only end with a 1, 5 or 9. And if it terminates in 5, it terminates in 15 or 65 only.

1 can be followed by any number : 10, 11, 12, 13, 14, 15, 16, 17, 18 or 19

5 can only be followed by 1 or 6 : 51 or 56

9 can be followed by any number : 90, 91, 92, 93, 94, 95, 96, 97, 98 or 99

There are no palindromic Quasi_Over_Squares of type x^2 + (x+9) of lengths 20, 22, 34.

Quasi_Over_Squares	Change of variables	CUDApalin parameters	Base Correction
x^2 + (x+0)	n.a.	A B C → 1 1 0	base = CUDAbase
x^2 + (x+1)	n.a.	A B C → 1 1 1	base = CUDAbase
x^2 + (x+2)	n.a.	A B C → 1 1 2	base = CUDAbase
x^2 + (x+3)	n.a.	A B C → 1 1 3	base = CUDAbase
x^2 + (x+4)	n.a.	A B C → 1 1 4	base = CUDAbase
x^2 + (x+5)	n.a.	A B C → 1 1 5	base = CUDAbase
x^2 + (x+6)	n.a.	A B C → 1 1 6	base = CUDAbase
x^2 + (x+7)	n.a.	A B C → 1 1 7	base = CUDAbase
x^2 + (x+8)	n.a.	A B C → 1 1 8	base = CUDAbase
x^2 + (x+9)	n.a.	A B C → 1 1 9	base = CUDAbase

Some people regard 1997 as a bad year !

So does Vincent Prosper because he figured out that after applying the "add & reverse" procedure to 1997,

this yearnumber never transformed into a palindrome. Follow this link to arrive at his website.

1997: A Bad Year

As for me, 1997 is a lucky year because of the following relations with the number of the beast 666 and other various palindromic numbers :

1413² + ( 1413 + 9 ) = 1997991 or from the right 1997991.

Note that 1413 = 666 + 747

30003² + ( 30003 + 1997 ) = 900212009.

Note that 1997 = 666 + 1331

and moreover 1331 = 11³ is a palindromic cube !

An infinite palindromic pattern resides in the list for case n^2 + (n + 2)

21² + 23 = 464
201² + 203 = 40604
2001² + 2003 = 4006004
20001² + 20003 = 400060004
200001² + 200003 = 40000600004
2000001² + 2000003 = 4000006000004
20000001² + 20000003 = 400000060000004

Some (in)finite palindromic pattern resides in the list for case n^2 + (n + 3)

1._
(QM3) 3009819902 [9059015845485109509] {L=19}
(QM3) 30009981999002 [900599019580454085910995009] {L=27}
(QM3) 300009998199990002 [90005999019958004540085991099950009] {L=35}
(QM3) 3000009999819999900002 [9000059999019995800045400085999109999500009] {L=43}
(QM3) 30000009999981999999000002 [900000599999019999580000454000085999910999995000009] {L=51}

2._
(QM3) 300990099009902 [90595039701990909910793059509] {L=29}
(QM3) 30009900990099002 [900594157435545090545534751495009] {L=33}
(QM3) 3000099009900990002 [9000594069208900509050098029604950009] {L=37}
(QM3) 300000990099009900002 [is no longer palindromic] {L=41}

An infinite palindromic pattern hides in the list for case n^2 + (n + 4)

20² + 24 = 424
200² + 204 = 40204
2000² + 2004 = 4002004
20000² + 20004 = 400020004
200000² + 200004 = 40000200004
2000000² + 2000004 = 4000002000004
20000000² + 20000004 = 400000020000004

A very nice but finite palindromic pattern hides in the list for case n^2 + (n + 6)

28² + 34 = 818
288² + 294 = 83238
2888² + 2894 = 8343438
28888² + 28894 = 834545438
288888² + 288894 = 83456565438
2888888² + 2888894 = 8345676765438
28888888² + 28888894 = 834567878765438
288888888² + 288888894 = 83456789898765438
alas
2888888888² + 2888888894 = 8345679010098765438 is no longer palindromic !

An infinite palindromic pattern hides in the list for case n^2 + (n + 7)

31² + 38 = 999
301² + 308 = 90909
3001² + 3008 = 9009009
30001² + 30008 = 900090009
300001² + 300008 = 90000900009
3000001² + 3000008 = 9000009000009
30000001² + 30000008 = 900000090000009

A second peculiar infinite palindromic pattern emerges as well.

3121_{00}_1208 = 9740648543458460479 which is basically a compressed form of 974064[1 + 7]54345[7 + 1]460479

3121_{000}_1208 = 9740641_{}_7543457_{}_1460479
3121_{0000}_1208 = 9740641_{0}_7543457_{0}_1460479
3121_{00000}_1208 = 9740641_{00}_7543457_{00}_1460479
or generally
3121_{0}_n_1208 = 9740641_{0}_n-3_7543457_{0}_n-3_1460479 ( for n>=3 )

An infinite palindromic pattern hides in the list for case n^2 + (n + 9)

30² + 39 = 939
300² + 309 = 90309
3000² + 3009 = 9003009
30000² + 30009 = 900030009
300000² + 300009 = 90000300009
3000000² + 3000009 = 9000003000009
30000000² + 30000009 = 900000030000009

The Table

Index Nr	Basenumber	Length
Index Nr	Palindromic Quasi_Over_Squares of form n^2+(n+X)	Length

	[QP1] Case X = 0 [Scanned exhaustively up to length 59]
See in-depth webpage about Palindromic Pronic Numbers

	[QM1] Case X = 1 [Scanned exhaustively up to length 53]
See in-depth webpage about Palindromic Quasi-Over-Squares

	[QM2] Case X = 2
One can find the regular numbers of the form n²+(n+2) at %N n^2 + (n+2). under A014206. The palindromic numbers of the form n²+(n+2) are categorised as follows : %N n^2 + (n+2) is a palindrome. under A027712. %N Palindromes of the form n^2 + (n+2). under A027713. More terms from Giovanni Resta, Aug 28, 2018. See Index Nrs 51 up to 65. More terms from Patrick De Geest, Sep 1, 2020. See Index Nrs 66 up to 115. More terms from Robert Xiao, Nov 3, 2022. See Index Nrs 116 up to 121. More terms from Robert Xiao, Nov 11, 2022. See Index Nrs 122 up to 128. More terms from Robert Xiao, Dec 6, 2022. See Index Nrs 129 up to 152. More terms from Patrick De Geest, Jun 21, 2023. See Index Nrs 153 up to 155. More terms from Patrick De Geest, Jul 18, 2023. See Index Nrs 156 up to 161.
161	2.916.941.228.048.406.027.740.141.832	28
161	8.508.546.127.888.543.060.000.205.907.095.020.000.603.458.887.216.458.058	55
160	2.105.878.593.908.461.957.725.397.981	28
160	4.434.724.652.281.880.828.482.876.291.926.782.848.280.881.822.564.274.344	55
159	2.000.000.000.000.000.000.000.000.001	28
159	4.000.000.000.000.000.000.000.000.006.000.000.000.000.000.000.000.000.004	55
158	1.590.449.007.023.765.386.552.303.249	28
158	2.529.528.043.942.881.319.886.728.507.058.276.889.131.882.493.408.259.252	55
157	1.489.727.359.201.790.342.383.089.279	28
157	2.219.287.604.754.340.068.700.850.059.500.580.078.600.434.574.067.829.122	55
156	1.483.733.601.665.779.326.753.416.620	28
156	2.201.465.400.712.105.517.353.667.074.707.663.537.155.012.170.045.641.022	55
155	291.819.736.041.306.538.408.058.187	27
155	85.158.758.343.217.822.268.333.031.213.033.386.222.871.234.385.785.158	53
154	208.232.426.734.519.414.742.680.588	27
154	43.360.743.543.746.995.891.455.860.006.855.419.859.964.734.534.706.334	53
153	200.000.000.000.000.000.000.000.001	27
153	40.000.000.000.000.000.000.000.000.600.000.000.000.000.000.000.000.004	53
152	149.374.451.201.321.447.016.114.920	27
152	22.312.726.671.695.962.285.645.833.833.854.658.226.959.617.662.721.322	53
151	20.184.103.716.273.036.994.718.973	26
151	407.398.042.829.267.022.695.499.959.994.596.220.762.928.240.893.704	51
150	20.000.000.000.000.000.000.000.001	26
150	400.000.000.000.000.000.000.000.060.000.000.000.000.000.000.000.004	51
149	16.950.149.078.625.980.485.603.755	26
149	287.307.553.787.645.175.186.196.828.691.681.571.546.787.355.703.782	51
148	8.973.684.520.672.509.625.913.622	25
148	80.527.013.876.557.408.839.676.399.367.693.880.475.567.831.072.508	50
147	2.920.302.583.592.557.260.579.152	25
147	8.528.167.179.737.364.886.640.530.350.466.884.637.379.717.618.258	49
146	2.153.012.016.959.597.668.794.321	25
146	4.635.460.745.172.434.879.800.352.530.089.784.342.715.470.645.364	49
145	2.074.849.351.833.902.559.760.688	25
145	4.304.999.832.805.565.571.528.799.978.251.755.655.082.389.994.034	49
144	2.000.000.000.000.000.000.000.001	25
144	4.000.000.000.000.000.000.000.006.000.000.000.000.000.000.000.004	49
143	1.650.258.386.595.090.091.043.629	25
143	2.723.352.742.527.429.822.694.638.364.962.289.247.252.472.533.272	49
142	1.637.749.528.521.602.840.444.739	25
142	2.682.223.518.172.732.395.755.732.375.575.932.372.718.153.222.862	49
141	1.626.164.912.369.999.442.359.235	25
141	2.644.412.322.223.327.965.385.210.125.835.697.233.222.232.144.462	49
140	1.581.919.878.671.183.336.539.550	25
140	2.502.470.502.535.051.408.159.044.409.518.041.505.352.050.742.052	49
139	1.580.455.679.910.094.737.787.659	25
139	2.497.840.156.160.079.835.357.317.137.535.389.700.616.510.487.942	49
138	221.912.986.021.509.668.199.131	24
138	49.245.373.364.982.745.396.339.693.369.354.728.946.337.354.294	47
137	208.498.909.605.413.220.335.111	24
137	43.471.795.306.646.273.234.619.891.643.237.264.660.359.717.434	47
136	200.000.000.000.000.000.000.001	24
136	40.000.000.000.000.000.000.000.600.000.000.000.000.000.000.004	47
135	169.034.548.441.728.779.604.819	24
135	28.572.678.566.899.153.393.308.880.339.335.199.866.587.627.582	47
134	67.230.171.214.418.445.395.551	23
134	4.519.895.921.520.018.544.969.449.694.458.100.251.295.989.154	46
133	64.231.123.411.050.024.609.228	23
133	4.125.637.214.645.538.548.618.888.168.458.355.464.127.365.214	46
132	47.060.003.163.260.717.494.904	23
132	2.214.643.897.726.108.736.838.778.386.378.016.277.983.464.122	46
131	28.340.760.432.776.860.355.257	23
131	803.198.701.908.050.453.059.545.950.354.050.809.107.891.308	45
130	21.013.528.000.013.139.582.706	23
130	441.568.359.007.336.217.978.222.879.712.633.700.953.865.144	45
129	20.000.000.000.000.000.000.001	23
129	400.000.000.000.000.000.000.060.000.000.000.000.000.000.004	45
128	4.757.677.656.778.346.810.404	22
128	22.635.496.685.807.900.793.566.539.700.970.858.669.453.622	44
127	4.715.988.110.384.558.673.804	22
127	22.240.543.857.288.520.366.666.666.302.588.275.834.504.222	44
126	2.838.747.628.261.247.913.577	22
126	8.058.488.096.958.860.174.044.404.710.688.596.908.848.508	43
125	2.000.000.000.000.000.000.001	22
125	4.000.000.000.000.000.000.006.000.000.000.000.000.000.004	43
124	1.614.610.539.612.041.804.460	22
124	2.606.967.194.626.288.816.955.596.188.826.264.917.696.062	43
123	642.382.560.558.903.872.228	21
123	412.655.354.110.213.800.784.487.008.312.011.453.556.214	42
122	527.378.686.600.101.977.845	21
122	278.128.279.080.048.581.444.444.185.840.080.972.821.872	42
121	221.301.942.040.661.354.538	21
121	48.974.549.550.968.237.449.094.473.286.905.594.547.984	41
120	207.569.859.046.680.002.063	21
120	43.085.246.384.658.603.895.059.830.685.648.364.258.034	41
119	200.000.000.000.000.000.001	21
119	40.000.000.000.000.000.000.600.000.000.000.000.000.004	41
118	165.711.647.551.849.788.445	21
118	27.460.350.134.348.483.984.348.938.484.343.105.306.472	41
117	67.656.578.638.660.502.376	20
117	4.577.412.633.089.252.596.996.952.529.803.362.147.754	40
116	45.435.227.161.435.625.399	20
116	2.064.359.867.211.257.597.887.957.521.127.689.534.602	40
115	22.349.935.885.854.845.656	20
115	499.519.634.101.822.224.454.422.228.101.436.915.994	39
114	21.648.788.975.466.017.946	20
114	468.670.064.104.258.998.989.899.852.401.460.076.864	39
113	20.000.000.000.000.000.001	20
113	400.000.000.000.000.000.060.000.000.000.000.000.004	39
112	15.682.422.422.343.540.315	20
112	245.938.373.032.823.434.777.434.328.230.373.839.542	39
111	15.647.015.327.334.577.784	20
111	244.829.088.653.843.204.373.402.348.356.880.928.442	39
110	14.681.808.231.390.847.410	20
110	215.555.492.943.336.042.818.240.633.349.294.555.512	39
109	14.468.011.600.019.886.099	20
109	209.323.359.658.309.984.636.489.903.856.953.323.902	39
108	Prime! 2.837.459.270.361.355.697	19
108	8.051.175.110.959.597.047.407.959.590.115.711.508	37
107	2.058.677.547.772.551.633	19
107	4.238.153.245.702.806.613.166.082.075.423.518.324	37
106	2.000.000.000.000.000.001	19
106	4.000.000.000.000.000.006.000.000.000.000.000.004	37
105	1.604.777.671.384.426.749	19
105	2.575.311.374.574.023.168.613.204.754.731.135.752	37
104	1.472.063.339.927.111.614	19
104	2.166.970.476.757.362.959.592.637.576.740.796.612	37
103	703.359.338.401.854.468	18
103	494.714.358.917.094.430.034.490.719.853.417.494	36
102	664.384.175.944.617.418	18
102	441.406.333.245.608.354.453.806.542.333.604.144	36
101	468.033.494.872.988.314	18
101	219.055.352.323.023.578.875.320.323.253.550.912	36
100	200.000.000.000.000.001	18
100	40.000.000.000.000.000.600.000.000.000.000.004	35
99	20.548.848.021.323.333	17
99	422.255.155.003.443.878.344.300.551.552.224	33
98	20.000.000.000.000.001	17
98	400.000.000.000.000.060.000.000.000.000.004	33
97	6.850.109.083.855.646	16
97	46.923.994.460.721.644.612.706.449.932.964	32
96	4.514.881.483.507.324	16
96	20.384.154.810.117.299.271.101.845.148.302	32
95	2.916.449.084.541.632	16
95	8.505.675.262.723.726.273.272.625.765.058	31
94	2.829.855.733.529.602	16
94	8.008.083.472.590.364.630.952.743.808.008	31
93	2.188.234.330.424.216	16
93	4.788.369.484.847.119.117.484.849.638.874	31
92	2.067.032.967.032.958	16
92	4.272.625.286.801.075.701.086.825.262.724	31
91	2.000.000.000.000.001	16
91	4.000.000.000.000.006.000.000.000.000.004	31
90	1.572.610.479.725.859	16
90	2.473.103.720.943.597.953.490.273.013.742	31
89	1.542.828.488.662.805	16
89	2.380.319.745.429.556.559.245.479.130.832	31
88	1.488.667.854.682.279	16
88	2.216.131.981.564.340.434.651.891.316.122	31
87	925.624.837.663.112	15
87	856.781.340.098.863.368.890.043.187.658	30
86	222.473.255.490.468	15
86	49.494.349.408.527.272.580.494.349.494	29
85	210.516.022.946.981	15
85	44.316.995.917.414.041.471.959.961.344	29
84	200.000.000.000.001	15
84	40.000.000.000.000.600.000.000.000.004	29
83	20.000.000.000.001	14
83	400.000.000.000.060.000.000.000.004	27
82	14.754.699.832.485	14
82	217.701.167.146.747.641.761.107.712	27
81	5.270.176.390.870	13
81	27.774.759.190.888.809.195.747.772	26
80	4.904.746.291.440	13
80	24.056.536.183.399.338.163.565.042	26
79	2.925.116.099.267	13
79	8.556.304.194.193.914.914.036.558	25
78	2.838.046.790.777	13
78	8.054.509.586.642.466.859.054.508	25
77	2.084.206.947.111	13
77	4.343.918.598.387.838.958.193.434	25
76	2.071.648.052.433	13
76	4.291.725.653.151.513.565.271.924	25
75	2.067.032.967.041	13
75	4.272.625.286.836.386.825.262.724	25
74	2.015.098.740.201	13
74	4.060.622.932.761.672.392.260.604	25
73	2.000.000.000.001	13
73	4.000.000.000.006.000.000.000.004	25
72	1.644.864.716.954	13
72	2.705.579.937.081.807.399.755.072	25
71	1.549.917.788.440	13
71	2.402.245.150.924.290.515.422.042	25
70	1.511.192.351.795	13
70	2.283.702.324.125.214.232.073.822	25
69	Prime! 899.201.757.557	12
69	808.563.800.794.497.008.365.808	24
68	Prime! 684.374.223.053	12
68	468.368.077.180.081.770.863.864	24
67	675.835.699.323	12
67	456.753.892.480.084.298.357.654	24
66	654.264.529.133	12
66	428.062.074.082.280.470.260.824	24
65	544.298.466.465	12
65	296.260.820.596.695.028.062.692	24
64	200.000.000.001	12
64	40.000.000.000.600.000.000.004	23
63	146.078.456.085	12
63	21.338.915.332.323.351.983.312	23
62	89.921.234.442	11
62	8.085.828.403.663.048.285.808	22
61	48.973.960.094	11
61	2.398.448.767.337.678.448.932	22
60	48.762.480.705	11
60	2.377.779.524.554.259.777.732	22
59	47.382.584.979	11
59	2.245.109.359.339.539.015.422	22
58	20.000.000.001	11
58	400.000.000.060.000.000.004	21
57	6.383.911.901	10
57	40.754.331.166.113.345.704	20
56	2.916.938.792	10
56	8.508.531.919.191.358.058	19
55	2.137.594.676	10
55	4.569.311.001.001.139.654	19
54	2.092.486.163	10
54	4.378.498.344.438.948.734	19
53	Prime! 2.089.713.863	10
53	4.366.904.031.304.096.634	19
52	2.069.010.866	10
52	4.280.805.965.695.080.824	19
51	2.067.032.958	10
51	4.272.625.251.525.262.724	19
50	2.000.000.001	10
50	4.000.000.006.000.000.004	19
49	1.553.608.459	10
49	2.413.699.245.429.963.142	19
48	1.434.631.499	10
48	2.058.167.539.357.618.502	19
47	528.342.929	9
47	279.146.251.152.641.972	18
46	482.441.669	9
46	232.749.964.469.947.232	18
45	223.314.956	9
45	49.869.569.796.596.894	17
44	213.934.623	9
44	45.768.023.132.086.754	17
43	200.000.001	9
43	40.000.000.600.000.004	17
42	161.280.539	9
42	26.011.412.421.411.062	17
41	92.610.852	8
41	8.576.770.000.776.758	16
40	48.829.930	8
40	2.384.362.112.634.832	16
39	29.287.052	8
39	857.731.444.137.758	15
38	22.012.038	8
38	484.529.838.925.484	15
37	21.855.108	8
37	477.645.767.546.774	15
36	21.147.906	8
36	447.233.949.332.744	15
35	20.000.001	8
35	400.000.060.000.004	15
34	17.101.809	8
34	292.471.888.174.292	15
33	14.842.995	8
33	220.314.515.413.022	15
32	2.000.001	7
32	4.000.006.000.004	13
31	1.651.754	7
31	2.728.292.928.272	13
30	1.620.660	7
30	2.626.540.456.262	13
29	501.474	6
29	251.476.674.152	12
28	Prime! 219.083	6
28	47.997.579.974	11
27	200.001	6
27	40.000.600.004	11
26	89.777	5
26	8.059.999.508	10
25	28.377	5
25	805.282.508	9
24	20.993	5
24	440.727.044	9
23	20.001	5
23	400.060.004	9
22	16.780	5
22	281.585.182	9
21	2.183	4
21	4.767.674	7
20	2.106	4
20	4.437.344	7
19	2.001	4
19	4.006.004	7
18	1.654	4
18	2.737.372	7
17	1.530	4
17	2.342.432	7
16	1.424	4
16	2.029.202	7
15	897	3
15	805.508	6
14	Prime! 479	3
14	229.922	6
13	292	3
13	85.558	5
12	203	3
12	41.414	5
11	201	3
11	40.604	5
10	92	2
10	8.558	4
9	50	2
9	2.552	4
8	21	2
8	464	3
7	15	2
7	242	3
6	14	2
6	212	3
5	6	1
5	44	2
4	4	1
4	22	2
3	Prime! 2	1
3	8	1
2	1	1
2	4	1
1	0	1
1	Prime! 2	1

	[QM3] Case X = 3
One can find the regular numbers of the form n²+(n+3) at %N n^2 + (n+3). under A027688. The palindromic numbers of the form n²+(n+3) are categorised as follows : %N n^2 + (n+3) is a palindrome. under A027714. %N Palindromes of the form n^2 + (n+3). under A027715. More terms from Giovanni Resta, Aug 29, 2018. See Index Nrs 38 up to 50. More terms from Patrick De Geest, Sep 1, 2020. See Index Nrs 51 up to 124. More terms from Robert Xiao, Nov 11, 2022. See Index Nrs 126 up to 188 except Nr 167 which was already known. More terms from Robert Xiao, Dec 6, 2022. See Index Nrs 189 up to 316 except Nr 286 which was already known. More terms from Patrick De Geest, Jun 22, 2023. See Index Nrs 317 up to 352 More terms from Patrick De Geest, Jul 18, 2023. See Index Nrs 353 up to 392

392	3.000.999.009.990.090.099.900.999.002	28
392	9.005.995.057.961.500.899.227.496.415.146.947.229.980.051.697.505.995.009	55
391	3.000.999.009.900.999.009.900.999.002	28
391	9.005.995.057.426.776.353.457.557.605.067.557.543.536.776.247.505.995.009	55
390	3.000.999.009.900.909.009.900.999.002	28
390	9.005.995.057.426.236.173.635.775.433.345.775.363.716.326.247.505.995.009	55
389	3.000.999.009.900.090.009.900.999.002	28
389	9.005.995.057.421.320.537.257.558.415.148.557.527.350.231.247.505.995.009	55
388	3.000.990.999.009.909.900.999.099.002	28
388	9.005.946.976.138.497.048.398.652.633.362.568.938.407.948.316.796.495.009	55
387	3.000.990.990.009.000.900.099.099.002	28
387	9.005.946.922.115.203.340.198.653.443.443.568.910.433.025.112.296.495.009	55
386	3.000.990.099.099.909.990.990.099.002	28
386	9.005.941.574.895.687.588.514.914.633.364.194.158.857.865.984.751.495.009	55
385	3.000.990.099.099.000.990.990.099.002	28
385	9.005.941.574.890.231.788.514.751.823.281.574.158.871.320.984.751.495.009	55
384	3.000.990.099.009.090.900.990.099.002	28
384	9.005.941.574.350.593.208.724.635.451.545.364.278.023.950.534.751.495.009	55
383	3.000.990.090.099.909.990.090.099.002	28
383	9.005.941.520.877.865.880.314.752.633.362.574.130.885.687.780.251.495.009	55
382	3.000.900.900.090.999.090.009.009.002	28
382	9.005.406.212.166.968.502.222.713.081.803.172.222.058.696.612.126.045.009	55
381	3.000.099.990.000.999.000.099.990.002	28
381	9.000.599.950.003.994.300.379.981.009.001.899.730.034.993.000.599.950.009	55
380	3.000.099.909.999.000.999.909.990.002	28
380	9.000.599.469.976.013.899.839.743.027.203.479.389.983.106.799.649.950.009	55
379	3.000.099.900.999.909.999.009.990.002	28
379	9.000.599.415.979.669.777.077.562.217.122.657.707.779.669.795.149.950.009	55
378	3.000.099.900.999.819.999.009.990.002	28
378	9.000.599.415.979.129.759.095.382.241.422.835.909.579.219.795.149.950.009	55
377	3.000.099.900.999.000.999.009.990.002	28
377	9.000.599.415.974.215.595.457.545.207.025.457.545.955.124.795.149.950.009	55
376	3.000.099.900.099.909.990.009.990.002	28
376	9.000.599.410.579.489.902.085.926.017.106.295.802.099.849.750.149.950.009	55
375	3.000.099.900.099.000.990.009.990.002	28
375	9.000.599.410.574.035.720.467.545.207.025.457.640.275.304.750.149.950.009	55
374	3.000.099.000.999.000.999.000.990.002	28
374	9.000.594.015.795.203.797.201.745.207.025.471.027.973.025.975.104.950.009	55
373	3.000.099.000.099.000.990.000.990.002	28
373	9.000.594.010.395.025.542.211.761.407.041.671.122.455.205.930.104.950.009	55
372	3.000.090.009.900.999.009.900.090.002	28
372	9.000.540.067.507.776.337.252.103.425.243.012.527.336.777.057.600.450.009	55
371	3.000.090.009.900.090.009.900.090.002	28
371	9.000.540.067.502.322.173.614.104.235.324.014.163.712.232.057.600.450.009	55
370	3.000.090.009.000.090.000.900.090.002	28
370	9.000.540.062.102.160.102.602.322.055.502.232.062.010.612.012.600.450.009	55
369	3.000.090.000.900.090.009.000.090.002	28
369	9.000.540.013.500.702.071.012.322.055.502.232.101.702.070.053.100.450.009	55
368	3.000.009.999.900.999.009.999.900.002	28
368	9.000.059.999.505.992.079.989.401.209.021.049.899.702.995.059.999.500.009	55
367	3.000.009.999.009.999.900.999.900.002	28
367	9.000.059.994.159.979.606.977.520.209.020.257.796.069.799.514.999.500.009	55
366	3.000.009.999.000.999.000.999.900.002	28
366	9.000.059.994.105.974.026.977.423.009.003.247.796.204.795.014.999.500.009	55
365	3.000.009.999.000.090.000.999.900.002	28
365	9.000.059.994.100.520.008.799.240.019.100.429.978.000.250.014.999.500.009	55
364	3.000.009.990.009.999.900.099.900.002	28
364	9.000.059.940.159.799.700.397.504.009.004.057.930.079.979.510.499.500.009	55
363	3.000.009.990.000.999.000.099.900.002	28
363	9.000.059.940.105.794.120.559.423.009.003.249.550.214.975.010.499.500.009	55
362	3.000.009.990.000.180.000.099.900.002	28
362	9.000.059.940.100.880.104.195.802.043.402.085.914.010.880.010.499.500.009	55
361	3.000.009.990.000.090.000.099.900.002	28
361	9.000.059.940.100.340.102.397.602.019.102.067.932.010.430.010.499.500.009	55
360	3.000.009.000.099.000.990.000.900.002	28
360	9.000.054.000.675.007.722.033.021.227.221.203.302.277.005.760.004.500.009	55
359	3.000.009.000.090.000.090.000.900.002	28
359	9.000.054.000.621.002.160.015.120.047.400.215.100.612.001.260.004.500.009	55
358	3.000.000.999.000.999.000.999.000.002	28
358	9.000.005.994.006.992.008.990.005.009.005.000.998.002.996.004.995.000.009	55
357	3.000.000.990.000.999.000.099.000.002	28
357	9.000.005.940.006.974.102.572.021.209.021.202.752.014.796.000.495.000.009	55
356	3.000.000.990.000.090.000.099.000.002	28
356	9.000.005.940.001.520.100.772.200.219.120.022.770.010.251.000.495.000.009	55
355	3.000.000.900.000.090.000.009.000.002	28
355	9.000.005.400.001.350.000.216.000.039.300.006.120.000.531.000.045.000.009	55
354	2.343.633.080.809.476.929.100.713.306	28
354	5.492.616.017.464.520.217.729.745.612.165.479.277.120.254.647.106.162.945	55
353	1.743.330.003.962.878.046.838.570.699	28
353	3.039.199.502.717.208.386.494.573.329.233.754.946.838.027.172.059.919.303	55
352	Prime! 300.990.099.099.090.900.900.990.097	27
352	Prime! 90.595.039.755.680.561.154.195.403.930.459.145.116.508.655.793.059.509	53
351	300.099.909.990.099.009.990.999.002	27
351	90.059.955.976.065.527.578.873.832.523.837.887.572.556.067.955.995.009	53
350	300.099.900.999.009.900.099.000.997	27
350	90.059.950.579.615.543.235.461.159.395.116.453.234.551.697.505.995.009	53
349	300.099.900.990.009.990.099.000.997	27
349	90.059.950.574.213.799.035.542.159.395.124.553.099.731.247.505.995.009	53
348	300.099.900.099.009.900.999.000.997	27
348	90.059.950.039.435.722.787.423.159.395.132.478.722.753.493.005.995.009	53
347	300.099.099.909.900.990.999.099.002	27
347	90.059.469.766.732.736.983.993.254.345.239.938.963.723.766.796.495.009	53
346	300.099.099.009.900.990.099.099.002	27
346	90.059.469.226.554.357.415.993.092.329.039.951.475.345.562.296.495.009	53
345	300.099.009.900.909.099.009.900.997	27
345	90.059.415.743.505.937.435.545.545.754.554.553.473.950.534.751.495.009	53
344	300.099.000.990.990.090.099.900.997	27
344	90.059.410.395.790.271.079.841.737.573.714.897.017.209.759.301.495.009	53
343	300.099.000.990.099.009.900.099.002	27
343	90.059.410.395.255.446.524.315.670.507.651.342.564.455.259.301.495.009	53
342	300.009.999.099.990.000.900.009.997	27
342	90.005.999.559.976.001.150.041.997.179.914.005.110.067.995.599.950.009	53
341	300.009.999.009.990.009.900.009.997	27
341	90.005.999.505.974.206.720.323.779.197.732.302.760.247.950.599.950.009	53
340	300.009.999.000.999.900.099.990.002	27
340	90.005.999.500.579.961.055.997.200.900.279.955.016.997.500.599.950.009	53
339	300.009.999.000.099.000.099.990.002	27
339	90.005.999.500.039.403.039.798.010.901.089.793.030.493.000.599.950.009	53
338	300.009.990.999.900.999.909.990.002	27
338	90.005.994.699.760.678.967.774.212.721.247.776.987.606.799.649.950.009	53
337	300.009.990.099.900.999.009.990.002	27
337	90.005.994.159.742.695.437.934.430.703.443.973.459.624.795.149.950.009	53
336	300.009.990.099.000.099.009.990.002	27
336	90.005.994.159.202.137.437.773.240.704.237.773.473.120.295.149.950.009	53
335	300.009.990.009.990.009.990.009.997	27
335	90.005.994.105.794.305.594.505.399.199.350.549.550.349.750.149.950.009	53
334	300.009.990.009.909.009.990.009.997	27
334	90.005.994.105.745.703.976.123.787.378.732.167.930.754.750.149.950.009	53
333	300.009.990.000.990.099.990.009.997	27
333	Prime! 90.005.994.100.394.179.776.204.779.197.740.267.797.149.300.149.950.009	53
332	300.009.900.999.900.999.900.990.002	27
332	90.005.940.697.970.398.980.194.050.705.049.108.989.307.979.604.950.009	53
331	300.009.900.999.009.900.099.009.997	27
331	90.005.940.697.435.721.453.448.739.393.784.435.412.753.479.604.950.009	53
330	300.009.900.990.009.990.099.009.997	27
330	90.005.940.692.035.597.237.329.739.393.792.373.279.553.029.604.950.009	53
329	300.009.900.099.900.999.000.990.002	27
329	90.005.940.157.952.577.450.354.430.703.445.305.477.525.975.104.950.009	53
328	300.009.900.099.000.099.000.990.002	27
328	90.005.940.157.412.019.612.355.240.704.255.321.691.021.475.104.950.009	53
327	300.009.900.009.900.990.000.990.002	27
327	90.005.940.103.950.790.040.294.050.705.049.204.009.705.930.104.950.009	53
326	300.009.900.009.000.090.000.990.002	27
326	90.005.940.103.410.232.202.457.022.722.075.420.223.201.430.104.950.009	53
325	300.000.999.990.999.909.999.900.002	27
325	90.000.599.995.599.927.999.841.002.920.014.899.972.999.559.999.500.009	53
324	300.000.999.009.990.009.900.099.997	27
324	90.000.599.406.992.026.900.199.579.197.599.100.962.029.960.499.500.009	53
323	300.000.999.000.999.900.099.900.002	27
323	90.000.599.401.597.943.057.741.400.900.414.775.034.979.510.499.500.009	53
322	300.000.999.000.099.000.099.900.002	27
322	90.000.599.401.057.401.257.742.210.901.224.775.210.475.010.499.500.009	53
321	300.000.990.009.990.009.990.099.997	27
321	90.000.594.006.974.125.774.379.579.197.597.347.752.147.960.049.500.009	53
320	300.000.990.000.099.000.009.900.002	27
320	900.00.594.001.039.500.201.960.030.903.006.910.200.593.010.049.500.009	53
319	300.000.099.000.099.000.099.000.002	27
319	90.000.059.400.069.201.079.002.030.903.020.097.010.296.000.495.000.009	53
318	300.000.090.000.099.000.009.000.002	27
318	90.000.054.000.067.500.023.220.012.921.002.232.000.576.000.045.000.009	53
317	240.781.061.176.902.353.671.153.083	27
317	57.975.519.421.475.193.851.969.411.811.496.915.839.157.412.491.557.975	53
316	30.838.426.999.727.240.504.327.987	26
316	951.008.579.817.506.052.408.398.050.893.804.250.605.718.975.800.159	51
315	30.009.990.999.009.009.990.999.002	26
315	900.599.559.760.601.797.498.562.353.265.894.797.106.067.955.995.009	51
314	30.009.990.990.099.900.990.999.002	26
314	900.599.559.225.877.235.779.554.252.455.977.532.778.522.955.995.009	51
313	30.009.990.009.900.099.000.999.002	26
313	900.599.500.394.303.744.135.992.070.299.531.447.303.493.005.995.009	51
312	30.009.900.999.099.909.990.099.002	26
312	900.594.157.975.777.775.824.374.252.473.428.577.777.579.751.495.009	51
311	30.009.900.999.090.909.990.099.002	26
311	900.594.157.975.237.597.606.390.535.093.606.795.732.579.751.495.009	51
310	30.009.900.999.009.009.990.099.002	26
310	900.594.157.970.321.975.822.746.151.647.228.579.123.079.751.495.009	51
309	30.009.900.990.099.900.990.099.002	26
309	900.594.157.435.599.017.743.358.050.853.347.710.995.534.751.495.009	51
308	30.009.900.990.009.000.990.099.002	26
308	900.594.157.430.143.217.743.366.151.663.347.712.341.034.751.495.009	51
307	30.009.900.900.909.090.090.099.002	26
307	900.594.152.082.384.217.026.912.717.219.620.712.483.280.251.495.009	51
306	30.009.900.099.099.909.900.099.002	26
306	900.594.103.957.956.782.042.754.252.457.240.287.659.759.301.495.009	51
305	30.009.900.099.009.009.900.099.002	26
305	900.594.103.952.500.982.204.746.151.647.402.289.005.259.301.495.009	51
304	30.009.900.090.099.900.900.099.002	26
304	900.594.103.417.778.040.161.754.252.457.161.040.877.714.301.495.009	51
303	30.009.900.090.009.000.900.099.002	26
303	900.594.103.412.322.240.325.382.353.283.523.042.223.214.301.495.009	51
302	30.006.690.109.888.660.569.252.802	26
302	900.401.451.350.889.956.509.102.474.201.905.659.988.053.154.104.009	51
301	30.000.999.900.099.900.099.990.002	26
301	900.059.995.005.794.215.779.630.090.036.977.512.497.500.599.950.009	51
300	30.000.999.900.009.000.099.990.002	26
300	900.059.995.000.340.033.997.800.191.008.799.330.043.000.599.950.009	51
299	30.000.999.000.099.900.009.990.002	26
299	900.059.941.003.995.200.199.630.090.036.991.002.599.300.149.950.009	51
298	30.000.990.099.990.999.900.990.002	26
298	900.059.406.979.757.986.237.404.171.404.732.689.757.979.604.950.009	51
297	30.000.990.099.981.999.900.990.002	26
297	900.059.406.979.217.968.415.604.414.406.514.869.712.979.604.950.009	51
296	30.000.990.009.990.999.000.990.002	26
296	900.059.401.579.579.722.337.242.171.242.733.227.975.975.104.950.009	51
295	30.000.990.009.981.999.000.990.002	26
295	900.059.401.579.039.704.517.062.414.260.715.407.930.975.104.950.009	51
294	30.000.990.009.909.099.000.990.002	26
294	900.059.401.574.665.560.173.612.353.216.371.065.566.475.104.950.009	51
293	30.000.990.009.900.099.000.990.002	26
293	900.059.401.574.125.542.353.434.070.434.353.245.521.475.104.950.009	51
292	30.000.099.900.999.990.099.900.002	26
292	900.005.994.069.979.615.793.022.090.220.397.516.979.960.499.500.009	51
291	30.000.099.900.099.900.099.900.002	26
291	900.005.994.015.974.035.954.050.090.050.459.530.479.510.499.500.009	51
290	30.000.099.900.009.000.099.900.002	26
290	900005994010520017.792.220.191.022.297.710.025.010.499.500.009	51
289	30.000.099.000.099.900.009.900.002	26
289	900.005.940.015.795.020.374.212.090.212.473.020.597.510.049.500.009	51
288	30.000.099.000.018.000.009.900.002	26
288	900.005.940.010.881.004.158.002.434.200.851.400.188.010.049.500.009	51
287	30.000.099.000.009.000.009.900.002	26
287	900.005.940.010.341.002.376.002.191.200.673.200.143.010.049.500.009	51
286	30.000.009.999.981.999.999.000.002	26
286	900.000.599.999.019.999.580.000.454.000.085.999.910.999.995.000.009	51
285	30.000.009.000.009.000.009.000.002	26
285	900.000.540.000.621.000.702.000.393.000.207.000.126.000.045.000.009	51
284	18.603.614.682.732.832.889.421.584	26
284	346.094.479.263.592.642.526.728.787.827.625.246.295.362.974.490.643	51
283	18.342.225.383.416.581.183.888.605	26
283	336.437.232.016.051.548.619.577.080.775.916.845.150.610.232.734.633	51
282	17.933.510.849.802.130.612.622.904	26
282	321.610.811.399.970.736.889.219.161.912.988.637.079.993.118.016.123	51
281	5.605.366.478.437.820.000.891.814	25
281	31.420.133.357.594.407.596.985.500.558.969.570.449.575.333.102.413	50
280	5.483.011.386.045.514.264.563.999	25
280	30.063.413.859.504.751.457.661.722.716.675.415.740.595.831.436.003	50
279	3.094.886.514.989.921.948.064.747	25
279	9.578.322.540.666.464.370.936.336.336.390.734.646.660.452.238.759	49
278	3.009.900.900.909.090.990.990.097	25
278	9.059.503.433.293.357.584.752.419.142.574.857.533.923.343.059.509	49
277	3.000.999.099.900.990.009.000.997	25
277	9.005.995.597.606.552.212.251.773.771.522.122.556.067.955.995.009	49
276	3.000.999.009.990.099.900.999.002	25
276	9.005.995.057.961.559.725.398.307.038.935.279.551.697.505.995.009	49
275	Prime! 3.000.999.009.900.990.099.000.997	25
275	9.005.995.057.426.722.870.253.393.933.520.782.276.247.505.995.009	49
274	3.000.999.009.000.999.099.000.997	25
274	9.005.995.052.024.978.671.223.773.773.221.768.794.202.505.995.009	49
273	3.000.999.000.990.099.000.999.002	25
273	9.005.995.003.943.572.224.778.307.038.774.222.753.493.005.995.009	49
272	3.000.990.990.099.009.900.900.997	25
272	9.005.946.922.655.435.741.059.175.719.501.475.345.562.296.495.009	49
271	3.000.990.990.009.099.900.900.997	25
271	9.005.946.922.115.797.541.227.655.567.221.457.975.112.296.495.009	49
270	3.000.990.099.909.090.009.900.997	25
270	9.005.941.579.752.370.039.451.855.581.549.300.732.579.751.495.009	49
269	3.000.990.099.009.900.990.099.002	25
269	9.005.941.574.355.455.347.514.905.094.157.435.545.534.751.495.009	49
268	Prime! 3.000.990.009.900.990.099.900.997	25
268	9.005.941.039.525.544.657.833.393.933.387.564.455.259.301.495.009	49
267	3.000.099.990.099.990.099.990.002	25
267	9.000.599.950.597.960.695.970.209.020.795.960.697.950.599.950.009	49
266	3.000.099.990.099.009.900.009.997	25
266	9.000.599.950.592.079.300.069.591.959.600.039.702.950.599.950.009	49
265	3.000.099.990.009.900.099.990.002	25
265	9.000.599.950.057.402.679.762.109.012.679.762.047.500.599.950.009	49
264	3.000.099.900.999.000.990.009.997	25
264	9.000.599.415.974.215.541.455.791.975.541.455.124.795.149.950.009	49
263	3.000.099.900.990.900.990.009.997	25
263	9.000.599.415.925.613.923.059.673.769.503.293.165.295.149.950.009	49
262	3.000.099.900.099.990.009.990.002	25
262	9.000.599.410.579.970.037.954.009.004.597.300.799.750.149.950.009	49
261	3.000.099.900.099.009.990.009.997	25
261	9.000.599.410.574.089.722.265.791.975.622.279.804.750.149.950.009	49
260	3.000.099.900.009.900.009.990.002	25
260	9.000.599.410.039.412.037.962.109.012.697.302.149.300.149.950.009	49
259	3.000.099.009.990.099.900.990.002	25
259	9.000.594.069.743.577.545.522.507.052.255.457.753.479.604.950.009	49
258	3.000.099.009.909.090.099.009.997	25
258	9.000.594.069.257.502.692.089.655.569.802.962.057.529.604.950.009	49
257	3.000.099.009.900.009.900.990.002	25
257	9.000.594.069.203.019.705.910.607.060.195.079.103.029.604.950.009	49
256	3.000.099.000.999.000.999.009.997	25
256	9.000.594.015.795.203.797.255.791.975.527.973.025.975.104.950.009	49
255	3.000.099.000.990.099.000.990.002	25
255	9.000.594.015.741.790.046.522.507.052.256.400.971.475.104.950.009	49
254	3.000.099.000.900.009.000.990.002	25
254	9.000.594.015.201.232.208.532.227.222.358.022.321.025.104.950.009	49
253	3.000.099.000.099.009.999.009.997	25
253	9.000.594.010.395.079.598.049.591.959.408.959.705.930.104.950.009	49
252	3.000.009.990.099.990.099.900.002	25
252	9.000.059.940.699.742.697.212.209.022.127.962.479.960.499.500.009	49
251	3.000.009.990.009.900.099.900.002	25
251	9.000.059.940.159.200.897.204.109.014.027.980.029.510.499.500.009	49
250	3.000.009.900.099.990.009.900.002	25
250	9.000.059.400.697.952.039.212.209.022.129.302.597.960.049.500.009	49
249	3.000.009.900.009.900.009.900.002	25
249	9.000.059.400.157.410.255.420.309.030.245.520.147.510.049.500.009	49
248	2.382.353.795.412.352.149.785.246	25
248	5.675.609.606.515.639.443.004.615.164.003.449.365.156.069.065.765	49
247	2.249.827.877.791.568.157.305.326	25
247	5.061.725.479.688.111.343.328.669.668.233.431.118.869.745.271.605	49
246	1.851.391.838.416.071.583.142.984	25
246	3.427.651.739.353.641.310.282.435.342.820.131.463.539.371.567.243	49
245	1.846.697.305.799.027.728.177.084	25
245	3.410.290.939.245.387.730.128.234.328.210.377.835.429.390.920.143	49
244	587.648.931.982.397.798.785.684	24
244	345.331.267.260.052.794.511.426.624.115.497.250.062.762.133.543	48
243	300.990.099.090.009.099.009.902	24
243	90.595.039.750.213.496.251.884.348.815.269.431.205.793.059.509	47
242	300.990.090.090.909.009.009.902	24
242	90.595.034.332.933.521.615.667.176.651.612.533.923.343.059.509	47
241	300.099.900.999.099.900.999.002	24
241	90.059.950.579.669.561.757.821.712.875.716.596.697.505.995.009	47
240	300.099.900.990.909.900.999.002	24
240	90.059.950.574.753.925.379.523.532.597.352.935.747.505.995.009	47
239	300.099.900.990.009.900.999.002	24
239	90.059.950.574.213.745.557.740.704.775.554.731.247.505.995.009	47
238	300.099.900.099.099.000.999.002	24
238	90.059.950.039.489.200.589.621.712.698.500.298.493.005.995.009	47
237	300.099.099.909.990.999.099.002	24
237	90.059.469.766.786.759.683.524.542.538.695.768.766.796.495.009	47
236	300.099.099.000.900.099.099.002	24
236	90.059.469.221.152.038.857.243.534.275.883.025.112.296.495.009	47
235	300.099.009.909.990.990.099.002	24
235	90.059.415.748.956.870.483.362.526.338.407.865.984.751.495.009	47
234	300.099.009.909.090.990.099.002	24
234	90.059.415.748.416.692.265.525.352.556.229.661.484.751.495.009	47
233	300.099.009.009.990.090.099.002	24
233	90.059.415.208.778.113.277.162.526.177.231.187.780.251.495.009	47
232	300.099.009.000.900.090.099.002	24
232	90.059.415.203.322.313.293.443.534.439.231.322.330.251.495.009	47
231	300.009.999.000.900.099.990.002	24
231	90.005.999.500.520.078.994.201.910.249.987.002.500.599.950.009	47
230	300.009.990.009.990.009.990.002	24
230	90.005.994.105.794.305.594.500.900.549.550.349.750.149.950.009	47
229	300.009.990.001.800.009.990.002	24
229	90.005.994.100.880.141.958.204.340.285.914.108.800.149.950.009	47
228	300.009.990.000.900.009.990.002	24
228	90.005.994.100.340.123.976.201.910.267.932.104.300.149.950.009	47
227	300.009.900.999.099.900.990.002	24
227	90.005.940.697.489.723.770.241.714.207.732.798.479.604.950.009	47
226	300.009.900.990.009.900.990.002	24
226	90.005.940.692.035.543.770.160.706.107.734.553.029.604.950.009	47
225	300.009.000.990.009.900.090.002	24
225	90.005.400.675.023.761.212.322.722.321.216.732.057.600.450.009	47
224	300.009.000.090.009.000.090.002	24
224	90.005.400.135.007.020.224.104.740.142.202.070.053.100.450.009	47
223	300.000.990.009.990.009.900.002	24
223	90.000.594.006.974.125.720.320.902.302.752.147.960.049.500.009	47
222	300.000.990.000.900.009.900.002	24
222	90.000.594.001.520.107.722.021.912.022.770.102.510.049.500.009	47
221	300.000.900.000.900.000.900.002	24
221	90.000.540.001.350.002.160.003.930.006.120.005.310.004.500.009	47
220	228.585.919.096.785.361.834.541	24
220	52.251.522.409.322.102.770.759.795.707.720.122.390.422.515.225	47
219	187.945.011.618.892.865.309.850	24
219	35.323.327.392.425.774.139.991.119.993.147.752.429.372.332.353	47
218	97.754.914.177.332.579.973.107	23
218	9.556.023.245.817.658.240.785.335.870.428.567.185.423.206.559	46
217	72.994.941.384.766.472.414.711	23
217	5.328.261.467.765.493.053.425.225.243.503.945.677.641.628.235	46
216	72.126.784.306.709.288.752.733	23
216	5.202.273.014.426.565.335.394.664.935.335.656.244.103.722.025	46
215	30.949.589.175.630.263.472.372	23
215	957.877.070.140.289.971.709.272.907.179.982.041.070.778.759	45
214	30.099.009.909.009.099.009.902	23
214	905.950.397.502.627.930.659.434.956.039.726.205.793.059.509	45
213	30.094.277.968.492.564.695.302	23
213	905.665.566.444.896.966.739.555.937.669.698.444.665.566.509	45
212	30.052.649.533.285.083.851.382	23
212	903.161.743.970.460.168.235.313.532.861.064.079.347.161.309	45
211	30.009.990.099.900.099.000.997	23
211	900.599.505.796.101.954.017.919.710.459.101.697.505.995.009	45
210	30.009.990.099.009.900.999.002	23
210	900.599.505.742.672.287.565.070.565.782.276.247.505.995.009	45
209	30.009.990.009.900.999.000.997	23
209	900.599.500.394.357.762.117.919.711.267.753.493.005.995.009	45
208	30.009.990.009.009.000.999.002	23
208	900.599.500.340.820.059.861.272.168.950.028.043.005.995.009	45
207	30.009.909.900.990.099.099.002	23
207	900.594.692.265.543.579.507.252.705.975.345.562.296.495.009	45
206	30.009.900.990.909.009.900.997	23
206	900.594.157.484.161.574.356.555.653.475.161.484.751.495.009	45
205	30.009.900.990.099.009.900.997	23
205	900.594.157.435.545.534.751.939.157.435.545.534.751.495.009	45
204	30.009.900.099.009.900.099.002	23
204	900.594.103.952.554.411.765.070.567.114.455.259.301.495.009	45
203	30.009.900.090.099.099.900.997	23
203	900.594.103.417.729.964.355.737.553.469.927.714.301.495.009	45
202	30.009.009.000.909.990.990.997	23
202	900.540.621.216.696.855.678.353.876.558.696.612.126.045.009	45
201	30.000.999.900.990.099.990.002	23
201	900.059.995.059.207.989.403.090.304.989.702.950.599.950.009	45
200	30.000.999.099.900.090.009.997	23
200	900.059.946.992.206.010.959.717.959.010.602.299.649.950.009	45
199	30.000.999.009.999.009.990.002	23
199	900.059.941.597.961.577.522.090.225.775.169.795.149.950.009	45
198	30.000.999.000.990.009.990.002	23
198	900.059.941.057.403.577.441.090.144.775.304.750.149.950.009	45
197	30.000.990.099.900.099.009.997	23
197	900.059.406.974.303.752.775.919.577.257.303.479.604.950.009	45
196	30.000.990.009.900.999.009.997	23
196	900.059.401.574.179.544.675.919.576.445.971.475.104.950.009	45
195	30.000.990.000.990.000.990.002	23
195	900.059.401.039.502.019.603.090.306.910.205.930.104.950.009	45
194	30.000.900.099.009.900.090.002	23
194	900.054.006.750.772.233.023.272.320.332.277.057.600.450.009	45
193	30.000.900.090.000.900.090.002	23
193	900.054.006.210.216.015.120.474.021.510.612.012.600.450.009	45
192	30.000.099.000.990.009.900.002	23
192	900.005.940.069.201.790.023.090.320.097.102.960.049.500.009	45
191	30.000.090.000.990.000.900.002	23
191	900.005.400.067.500.232.201.292.102.232.005.760.004.500.009	45
190	17.788.105.396.821.095.046.385	23
190	316.416.693.608.415.767.267.151.762.767.514.806.396.614.613	45
189	17.475.123.748.007.910.457.875	23
189	305.379.950.008.190.039.964.555.469.930.091.800.059.973.503	45
188	3.009.909.909.090.909.909.902	22
188	9.059.557.660.843.649.558.291.928.559.463.480.667.559.509	43
187	3.009.909.909.000.909.909.902	22
187	9.059.557.660.301.865.774.663.664.775.681.030.667.559.509	43
186	3.009.909.900.909.009.909.902	22
186	9.059.557.611.590.085.854.853.584.585.800.951.167.559.509	43
185	3.006.010.168.205.571.584.382	22
185	9.036.097.131.355.288.769.853.589.678.825.531.317.906.309	43
184	3.000.999.099.000.990.999.002	22
184	9.005.995.592.204.759.775.227.225.779.574.022.955.995.009	43
183	3.000.999.000.999.000.999.002	22
183	9.005.995.003.997.001.999.009.009.991.007.993.005.995.009	43
182	3.000.990.099.909.990.099.002	22
182	9.005.941.579.757.772.356.417.146.532.777.579.751.495.009	43
181	3.000.990.099.819.990.099.002	22
181	9.005.941.579.217.594.138.441.448.314.957.129.751.495.009	43
180	3.000.990.099.000.990.099.002	22
180	9.005.941.574.301.972.355.607.065.532.791.034.751.495.009	43
179	3.000.990.009.909.900.099.002	22
179	9.005.941.039.579.022.294.417.144.922.209.759.301.495.009	43
178	3.000.990.009.000.900.099.002	22
178	9.005.941.034.123.222.457.227.227.542.223.214.301.495.009	43
177	3.000.900.990.999.099.009.002	22
177	9.005.406.757.779.374.511.445.441.154.739.777.576.045.009	43
176	3.000.900.990.090.099.009.002	22
176	9.005.406.752.323.736.510.635.360.156.373.232.576.045.009	43
175	3.000.900.900.090.009.009.002	22
175	9.005.406.212.161.026.232.255.522.326.201.612.126.045.009	43
174	3.000.900.090.090.090.009.002	22
174	9.005.401.350.702.710.332.255.522.330.172.070.531.045.009	43
173	3.000.099.990.999.099.990.002	22
173	9.000.599.955.992.799.841.029.201.489.972.995.599.950.009	43
172	3.000.099.900.999.009.990.002	22
172	9.000.599.415.974.269.543.209.023.459.624.795.149.950.009	43
171	3.000.099.900.090.009.990.002	22
171	9.000.599.410.520.087.924.019.104.297.800.250.149.950.009	43
170	3.000.099.000.999.000.990.002	22
170	9.000.594.015.795.203.743.209.023.473.025.975.104.950.009	43
169	3.000.099.000.180.000.990.002	22
169	9.000.594.010.881.041.580.243.420.851.401.880.104.950.009	43
168	3.000.099.000.090.000.990.002	22
168	9.000.594.010.341.023.760.219.120.673.201.430.104.950.009	43
167	3.000.009.999.819.999.900.002	22
167	9.000.059.999.019.995.800.045.400.085.999.109.999.500.009	43
166	3.000.009.000.090.000.900.002	22
166	9.000.054.000.621.007.020.039.300.207.001.260.004.500.009	43
165	2.375.578.106.375.977.215.853	22
165	5.643.371.339.492.873.720.814.180.273.782.949.331.733.465	43
164	2.360.575.773.314.734.247.376	22
164	5.572.317.981.560.455.607.679.767.065.540.651.897.132.755	43
163	1.923.599.756.208.458.048.829	22
163	3.700.236.022.085.239.239.772.779.329.325.802.206.320.073	43
162	1.741.168.540.460.336.028.699	22
162	3.031.667.886.288.776.822.212.122.286.778.826.887.661.303	43
161	953.298.840.362.417.450.357	21
161	908.778.679.036.329.870.174.471.078.923.630.976.877.809	42
160	301.427.718.106.492.371.317	21
160	90.858.669.242.887.028.952.625.982.078.824.296.685.809	41
159	300.990.099.090.900.990.097	21
159	90.595.039.750.750.397.025.552.079.305.705.793.059.509	41
158	Prime! 300.990.090.090.990.990.097	21
158	90.595.034.332.982.872.605.550.627.828.923.343.059.509	41
157	300.099.909.990.009.000.997	21
157	90.059.955.976.011.504.197.179.140.511.067.955.995.009	41
156	300.099.900.990.099.000.997	21
156	90.059.950.574.267.223.359.195.332.276.247.505.995.009	41
155	300.099.900.099.000.999.002	21
155	90.059.950.039.430.379.810.901.897.303.493.005.995.009	41
154	300.099.099.900.999.099.002	21
154	90.059.469.761.389.837.432.723.473.898.316.796.495.009	41
153	300.099.099.009.900.900.997	21
153	90.059.469.226.554.303.937.373.930.345.562.296.495.009	41
152	300.099.009.900.990.099.002	21
152	90.059.415.743.554.553.470.707.435.545.534.751.495.009	41
151	300.099.000.990.099.900.997	21
151	90.059.410.395.255.981.359.195.318.955.259.301.495.009	41
150	300.090.099.009.900.990.997	21
150	90.054.067.523.772.179.737.373.797.127.732.576.045.009	41
149	300.090.009.009.909.990.997	21
149	90.054.013.507.567.859.575.357.595.876.570.531.045.009	41
148	300.009.900.999.900.990.002	21
148	90.005.940.697.970.393.040.904.039.307.979.604.950.009	41
147	300.009.900.909.099.009.997	21
147	90.005.940.643.487.406.985.358.960.478.434.604.950.009	41
146	300.009.900.099.000.990.002	21
146	90.005.940.157.412.554.230.903.245.521.475.104.950.009	41
145	300.009.000.990.099.909.997	21
145	90.005.400.675.077.768.777.177.786.777.057.600.450.009	41
144	240.280.211.058.694.930.483	21
144	57.734.579.826.410.981.565.856.518.901.462.897.543.775	41
143	189.944.266.461.823.324.539	21
143	36.078.824.361.720.141.015.951.014.102.716.342.887.063	41
142	181.513.572.458.558.855.479	21
142	32.947.176.986.668.495.870.907.859.486.668.967.174.923	41
141	178.710.345.804.265.977.810	21
141	31.937.387.697.480.326.379.397.362.308.479.678.373.913	41
140	72.327.492.042.616.761.241	20
140	5.231.266.105.174.790.917.337.190.974.715.016.621.325	40
139	30.099.009.099.909.009.902	20
139	905.950.348.796.405.386.454.683.504.697.843.059.509	39
138	30.009.990.099.900.999.002	20
138	900.599.505.796.155.972.090.279.551.697.505.995.009	39
137	30.009.990.009.000.999.002	20
137	900.599.500.340.339.780.191.087.933.043.005.995.009	39
136	30.009.909.990.999.099.002	20
136	900.594.697.667.867.542.373.245.768.766.796.495.009	39
135	30.009.909.981.999.099.002	20
135	900.594.697.127.689.162.616.261.986.721.796.495.009	39
134	30.009.900.990.990.099.002	20
134	900.594.157.489.028.526.171.625.820.984.751.495.009	39
133	30.009.900.909.090.099.002	20
133	900.594.152.573.406.750.555.057.604.375.251.495.009	39
132	30.009.900.900.090.099.002	20
132	900.594.152.033.228.534.272.435.822.330.251.495.009	39
131	30.000.990.099.900.990.002	20
131	900.059.406.974.357.214.090.412.753.479.604.950.009	39
130	30.000.990.009.000.990.002	20
130	900.059.401.520.177.222.191.222.771.025.104.950.009	39
129	30.000.900.009.000.090.002	20
129	900.054.001.350.021.600.393.006.120.053.100.450.009	39
128	24.074.611.755.709.552.708	20
128	579.586.931.188.148.591.979.195.841.881.139.685.975	39
127	18.067.816.535.853.143.779	20
127	326.445.994.373.248.296.797.692.842.373.499.544.623	39
126	17.642.418.543.871.212.010	20
126	311.254.932.077.130.816.707.618.031.770.239.452.113	39
125	6.295.866.490.138.952.534	19
125	39.637.934.861.654.573.311.337.545.616.843.973.693	38
124	3.009.909.909.909.909.902	19
124	9.059.557.665.773.881.945.491.883.775.667.559.509	37
123	3.009.900.990.900.990.097	19
123	9.059.503.975.026.762.073.702.676.205.793.059.509	37
122	3.009.900.909.909.009.902	19
122	9.059.503.487.471.085.745.475.801.747.843.059.509	37
121	3.000.999.009.900.999.002	19
121	9.005.995.057.426.776.309.036.776.247.505.995.009	37
120	3.000.990.990.099.099.002	19
120	9.005.946.922.655.970.527.250.795.562.296.495.009	37
119	3.000.990.099.009.900.997	19
119	9.005.941.574.355.455.391.935.545.534.751.495.009	37
118	3.000.990.090.909.900.997	19
118	9.005.941.525.739.415.853.585.149.375.251.495.009	37
117	3.000.990.009.900.099.002	19
117	9.005.941.039.520.196.309.036.910.259.301.495.009	37
116	3.000.900.990.099.009.002	19
116	9.005.406.752.377.212.527.252.127.732.576.045.009	37
115	3.000.900.090.090.009.002	19
115	9.005.401.350.702.224.147.414.222.070.531.045.009	37
114	3.000.099.009.900.990.002	19
114	9.000.594.069.208.900.509.050.098.029.604.950.009	37
113	3.000.090.009.900.090.002	19
113	9.000.540.067.502.322.129.212.232.057.600.450.009	37
112	1.987.476.933.990.142.634	19
112	3.950.064.563.142.857.782.877.582.413.654.600.593	37
111	1.770.410.114.442.237.085	19
111	Prime! 3.134.351.973.319.375.014.105.739.133.791.534.313	37
110	300.990.990.909.909.902	18
110	90.595.576.608.929.465.556.492.980.667.559.509	35
109	300.900.909.090.900.902	18
109	90.541.357.091.730.609.390.603.719.075.314.509	35
108	300.099.900.900.999.002	18
108	90.059.950.520.789.421.912.498.702.505.995.009	35
107	300.099.009.990.099.002	18
107	90.059.415.797.037.540.904.573.079.751.495.009	35
106	300.099.001.800.099.002	18
106	90.059.410.881.415.824.342.851.418.801.495.009	35
105	300.099.000.900.099.002	18
105	90.059.410.341.237.621.912.673.214.301.495.009	35
104	300.090.099.099.009.002	18
104	90.054.067.577.253.043.734.035.277.576.045.009	35
103	300.090.090.009.009.002	18
103	90.054.062.121.615.124.742.151.612.126.045.009	35
102	300.009.998.199.990.002	18
102	90.005.999.019.958.004.540.085.991.099.950.009	35
101	300.009.000.900.090.002	18
101	90.005.400.621.070.203.930.207.012.600.450.009	35
100	30.099.099.090.090.097	17
100	905.955.766.035.062.535.260.530.667.559.509	33
99	30.099.090.099.090.097	17
99	905.955.224.793.143.535.341.397.422.559.509	33
98	30.099.009.090.990.097	17
98	905.950.348.259.504.535.405.952.843.059.509	33
97	30.099.009.009.009.902	17
97	905.950.343.324.459.272.954.423.343.059.509	33
96	Prime! 30.090.090.909.099.097	17
96	905.413.570.917.848.151.848.719.075.314.509	33
95	30.009.990.990.999.002	17
95	900.599.559.279.841.292.148.972.955.995.009	33
94	30.009.909.900.900.997	17
94	900.594.692.260.195.717.591.062.296.495.009	33
93	30.009.900.990.099.002	17
93	900.594.157.435.545.090.545.534.751.495.009	33
92	Prime! 30.009.009.900.990.997	17
92	900.540.675.237.775.717.577.732.576.045.009	33
91	22.797.812.361.579.671	17
91	519.740.248.473.794.878.497.374.842.047.915	33
90	22.683.451.840.157.828	17
90	514.538.987.384.759.575.957.483.789.835.415	33
89	19.007.389.738.417.935	17
89	361.280.864.668.115.434.511.866.468.082.163	33
88	17.587.931.732.323.900	17
88	309.335.342.620.885.999.588.026.243.533.903	33
87	3.009.909.909.909.902	16
87	9.059.557.665.773.837.383.775.667.559.509	31
86	3.009.900.909.009.902	16
86	9.059.503.482.058.637.368.502.843.059.509	31
85	3.009.090.090.090.902	16
85	9.054.623.170.283.275.723.820.713.264.509	31
84	3.009.009.090.900.902	16
84	9.054.135.709.124.275.724.219.075.314.509	31
83	3.000.990.999.099.002	16
83	9.005.946.976.673.229.223.766.796.495.009	31
82	3.000.990.090.099.002	16
82	9.005.941.520.872.419.142.780.251.495.009	31
81	3.000.900.090.009.002	16
81	9.005.401.350.216.039.306.120.531.045.009	31
80	2.434.467.459.876.868	16
80	5.926.631.813.199.332.339.913.181.366.295	31
79	2.328.650.332.630.593	16
79	5.422.612.371.660.573.750.661.732.162.245	31
78	1.746.916.031.844.124	16
78	3.051.715.622.314.022.204.132.265.171.503	31
77	300.990.990.090.097	15
77	90.595.576.115.417.171.451.167.559.509	29
76	300.990.099.009.902	15
76	90.595.039.701.990.909.910.793.059.509	29
75	300.990.090.990.097	15
75	90.595.034.874.227.172.247.843.059.509	29
74	300.900.909.099.097	15
74	Prime! 90.541.357.096.663.336.669.075.314.509	29
73	300.090.099.009.002	15
73	90.054.067.523.232.923.232.576.045.009	29
72	229.001.028.816.941	15
72	52.441.471.199.217.671.299.117.414.425	29
71	198.267.378.873.165	15
71	39.309.953.525.235.353.252.535.990.393	29
70	196.911.378.423.380	15
70	38.774.090.952.595.759.525.909.047.783	29
69	185.315.401.886.740	15
69	34.341.798.176.444.144.467.189.714.343	29
68	175.962.987.683.099	15
68	30.962.973.034.362.626.343.037.926.903	29
67	30.099.009.009.902	14
67	905.950.343.378.191.873.343.059.509	27
66	30.090.990.990.902	14
66	905.467.738.814.575.418.837.764.509	27
65	30.090.090.900.902	14
65	905.413.570.424.575.424.075.314.509	27
64	30.009.981.999.002	14
64	900.599.019.580.454.085.910.995.009	27
63	30.009.009.009.002	14
63	900.540.621.702.393.207.126.045.009	27
62	19.017.332.697.439	14
62	361.658.942.925.101.529.249.856.163	27
61	18.349.377.330.605	14
61	336.699.648.420.939.024.846.996.633	27
60	17.601.866.803.275	14
60	309.825.714.960.252.069.417.528.903	27
59	7.095.660.661.226	13
59	50.348.400.219.277.291.200.484.305	26
58	3.086.915.322.647	13
58	9.529.046.209.195.919.026.409.259	25
57	3.085.682.084.872	13
57	9.521.433.928.903.098.293.341.259	25
56	3.009.909.909.902	13
56	9.059.557.665.729.275.667.559.509	25
55	3.009.909.090.097	13
55	9.059.552.730.651.560.372.559.509	25
54	3.009.090.090.902	13
54	9.054.623.175.167.615.713.264.509	25
53	3.009.009.099.097	13
53	9.054.135.758.451.548.575.314.509	25
52	1.953.167.924.219	13
52	3.814.864.940.199.910.494.684.183	25
51	1.897.132.914.325	13
51	3.599.113.294.617.164.923.119.953	25
50	1.755.185.230.175	13
50	3.080.675.192.226.222.915.760.803	25
49	300.990.909.902	12
49	90.595.527.843.934.872.559.509	23
48	300.900.900.902	12
48	90.541.352.163.936.125.314.509	23
47	181.723.112.005	12
47	33.023.289.436.963.498.232.033	23
46	71.171.663.326	11
46	5.065.405.660.660.665.045.605	22
45	57.747.550.569	11
45	3.334.779.596.776.959.774.333	22
44	30.090.990.902	11
44	905.467.733.494.337.764.509	21
43	22.486.248.626	11
43	505.631.377.292.773.136.505	21
42	19.707.956.144	11
42	388.403.535.393.535.304.883	21
41	3.009.819.902	10
41	9.059.015.845.485.109.509	19
40	3.009.090.902	10
40	9.054.628.059.508.264.509	19
39	2.411.508.138	10
39	5.815.371.502.051.735.185	19
38	2.381.776.121	10
38	5.672.857.492.947.582.765	19
37	2.315.681.863	10
37	5.362.382.492.942.832.635	19
36	727.913.433	9
36	529.857.966.669.758.925	18
35	726.714.741	9
35	528.114.315.513.411.825	18
34	589.167.859	9
34	347.118.766.667.811.743	18
33	549.199.524	9
33	301.620.117.711.026.103	18
32	Prime! 309.230.287	9
32	95.623.370.707.332.659	17
31	230.098.566	9
31	52.945.350.305.354.925	17
30	177.865.385	9
30	31.636.095.359.063.613	17
29	76.675.186	8
29	5.879.084.224.809.785	16
28	62.127.180	8
28	3.859.786.556.879.583	16
27	30.909.092	8
27	955.371.999.173.559	15
26	18.886.025	8
26	356.681.959.186.653	15
25	17.605.724	8
25	309.961.535.169.903	15
24	5.492.899	7
24	30.171.944.917.103	14
23	3.093.852	7
23	9.571.923.291.759	13
22	598.350	6
22	358.023.320.853	12
21	237.721	6
21	56.511.511.565	11
20	Prime! 230.663	6
20	53.205.650.235	11
19	75.146	5
19	5.646.996.465	10
18	73.188	5
18	5.356.556.535	10
17	30.947	5
17	957.747.759	9
16	23.111	5
16	534.141.435	9
15	6.154	4
15	37.877.873	8
14	2.431	4
14	5.912.195	7
13	753	3
13	567.765	6
12	243	3
12	59.295	5
11	184	3
11	34.043	5
10	Prime! 179	3
10	32.223	5
9	175	3
9	Prime! 30.803	5
8	Prime! 71	2
8	5.115	4
7	60	2
7	3.663	4
6	Prime! 23	2
6	555	3
5	Prime! 19	2
5	Prime! 383	3
4	Prime! 5	1
4	33	2
3	Prime! 2	1
3	9	1
2	1	1
2	Prime! 5	1
1	0	1
1	Prime! 3	1


	[QM4] Case X = 4
One can find the regular numbers of the form n²+(n+4) at %N n^2 + (n+4). under A027689. The palindromic numbers of the form n²+(n+4) are categorised as follows : %N n^2 + (n+4) is a palindrome. under A027716. %N Palindromes of the form n^2 + (n+4). under A027717. More terms from Giovanni Resta, Aug 29, 2018. See Index Nrs 33 up to 36. More terms from Patrick De Geest, Sep 1, 2020. See Index Nrs 37 up to 57. More terms from Robert Xiao, Nov 11, 2022. See Index Nrs 58 up to 70. More terms from Robert Xiao, Dec 6, 2022. See Index Nrs 71 up to 77. More terms from Patrick De Geest, Jun 22, 2023. See Index Nrs 78 up to 81. More terms from Patrick De Geest, Jul 18, 2023. See Index Nr 82.
82	2.000.000.000.000.000.000.000.000.000	28
82	4.000.000.000.000.000.000.000.000.002.000.000.000.000.000.000.000.000.004	55
81	263.599.064.210.346.216.030.151.843	27
81	69.484.466.652.570.227.367.225.174.047.152.276.372.207.525.666.448.496	53
80	259.161.643.409.192.300.142.862.316	27
80	67.164.757.414.553.346.783.385.003.830.058.338.764.335.541.475.746.176	53
79	209.723.971.282.573.306.843.931.969	27
79	43.984.144.130.533.633.099.669.453.535.496.699.033.633.503.144.148.934	53
78	200.000.000.000.000.000.000.000.000	27
78	40.000.000.000.000.000.000.000.000.200.000.000.000.000.000.000.000.004	53
77	20.000.000.000.000.000.000.000.000	26
77	400.000.000.000.000.000.000.000.020.000.000.000.000.000.000.000.004	51
76	2.216.679.932.356.152.498.755.090	25
76	4.913.669.922.510.476.817.570.972.790.757.186.740.152.299.663.194	49
75	2.000.000.000.000.000.000.000.000	25
75	4.000.000.000.000.000.000.000.002.000.000.000.000.000.000.000.004	49
74	213.889.222.221.047.345.477.749	24
74	45.748.599.382.324.573.547.664.046.674.537.542.328.399.584.754	47
73	200.000.000.000.000.000.000.000	24
73	40.000.000.000.000.000.000.000.200.000.000.000.000.000.000.004	47
72	25.392.831.461.173.895.119.806	23
72	644.795.889.615.582.773.459.303.954.377.285.516.988.597.446	45
71	20.000.000.000.000.000.000.000	23
71	400.000.000.000.000.000.000.020.000.000.000.000.000.000.004	45
70	2.520.666.561.707.904.605.811	22
70	6.353.759.915.312.349.657.994.997.569.432.135.199.573.536	43
69	2.000.000.000.000.000.000.000	22
69	4.000.000.000.000.000.000.002.000.000.000.000.000.000.004	43
68	245.706.621.055.561.922.226	21
68	60.371.743.630.541.505.336.163.350.514.503.634.717.306	41
67	212.324.863.448.228.312.574	21
67	45.081.847.638.308.799.321.112.399.780.383.674.818.054	41
66	211.254.379.519.623.010.415	21
66	44.628.412.866.220.914.028.882.041.902.266.821.482.644	41
65	208.827.701.545.597.915.394	21
65	43.609.008.932.817.317.982.128.971.371.823.980.090.634	41
64	200.000.000.000.000.000.000	21
64	40.000.000.000.000.000.000.200.000.000.000.000.000.004	41
63	25.093.514.750.456.275.558	20
63	629.684.482.531.366.677.414.776.663.135.284.486.926	39
62	24.779.742.894.344.292.828	20
62	614.035.657.909.806.470.777.074.608.909.756.530.416	39
61	24.758.349.323.692.745.603	20
61	612.975.861.233.997.033.616.330.799.332.168.579.216	39
60	22.326.360.372.535.840.790	20
60	498.466.367.484.338.727.565.727.833.484.763.664.894	39
59	20.019.380.272.243.422.999	20
59	400.775.586.484.689.149.171.941.986.484.685.577.004	39
58	20.000.000.000.000.000.000	20
58	400.000.000.000.000.000.020.000.000.000.000.000.004	39
57	2.456.920.322.636.915.226	19
57	6.036.457.471.786.283.611.163.826.871.747.546.306	37
56	2.019.265.573.385.942.299	19
56	4.077.433.455.861.658.326.238.561.685.543.347.704	37
55	2.000.000.000.000.000.000	19
55	4.000.000.000.000.000.002.000.000.000.000.000.004	37
54	251.777.501.269.233.963	18
54	63.391.910.145.379.110.101.197.354.101.919.336	35
53	200.000.000.000.000.000	18
53	40.000.000.000.000.000.200.000.000.000.000.004	35
52	21.502.431.241.622.339	17
52	462.354.549.300.696.424.696.003.945.453.264	33
51	20.000.000.000.000.000	17
51	400.000.000.000.000.020.000.000.000.000.004	33
50	2.464.706.598.254.901	16
50	6.074.778.615.481.248.421.845.168.774.706	31
49	2.209.415.043.638.519	16
49	4.881.514.835.056.201.026.505.384.151.884	31
48	2.103.611.085.905.640	16
48	4.425.179.600.745.108.015.470.069.715.244	31
47	2.000.000.000.000.000	16
47	4.000.000.000.000.002.000.000.000.000.004	31
46	260.565.021.991.216	15
46	67.894.130.685.283.138.258.603.149.876	29
45	220.867.190.255.619	15
45	48.782.315.731.412.021.413.751.328.784	29
44	210.855.962.500.840	15
44	44.460.236.922.155.855.122.963.206.444	29
43	200.000.000.000.000	15
43	40.000.000.000.000.200.000.000.000.004	29
42	25.142.773.284.288	14
42	632.159.048.425.131.524.840.951.236	27
41	25.075.537.810.133	14
41	628.782.596.467.434.764.695.287.826	27
40	24.884.321.704.671	14
40	619.229.466.701.585.107.664.922.916	27
39	20.217.027.652.824	14
39	408.728.207.115.070.511.702.827.804	27
38	20.139.827.049.124	14
38	405.612.633.568.646.865.336.216.504	27
37	20.000.000.000.000	14
37	400.000.000.000.020.000.000.000.004	27
36	2.537.387.874.018	13
36	6.438.337.223.216.123.227.338.346	25
35	2.451.351.151.126	13
35	6.009.122.466.129.216.642.219.006	25
34	2.007.806.131.300	13
34	4.031.285.460.887.880.645.821.304	25
33	2.000.000.000.000	13
33	4.000.000.000.002.000.000.000.004	25
32	200.000.000.000	12
32	40.000.000.000.200.000.000.004	23
31	24.784.431.171	11
31	614.268.028.494.820.862.416	21
30	21.572.321.960	11
30	465.365.074.767.470.563.564	21
29	20.349.812.814	11
29	414.114.881.585.188.411.414	21
28	20.102.030.400	11
28	404.091.626.222.626.190.404	21
27	20.000.000.000	11
27	400.000.000.020.000.000.004	21
26	2.094.600.194	10
26	4.387.349.974.799.437.834	19
25	2.000.000.000	10
25	4.000.000.002.000.000.004	19
24	205.705.704	9
24	42.314.836.863.841.324	17
23	200.000.000	9
23	40.000.000.200.000.004	17
22	25.882.353	8
22	669.896.222.698.966	15
21	20.000.000	8
21	400.000.020.000.004	15
20	2.620.486	7
20	6.866.949.496.686	13
19	2.490.266	7
19	6.201.427.241.026	13
18	2.155.139	7
18	4.644.626.264.464	13
17	2.000.000	7
17	4.000.002.000.004	13
16	218.354	6
16	47.678.687.674	11
15	205.704	6
15	42.314.341.324	11
14	202.885	6
14	41.162.526.114	11
13	200.000	6
13	40.000.200.004	11
12	20.604	5
12	424.545.424	9
11	20.000	5
11	400.020.004	9
10	2.613	4
10	6.830.386	7
9	Prime! 2.551	4
9	6.510.156	7
8	2.234	4
8	4.992.994	7
7	2.000	4
7	4.002.004	7
6	261	3
6	68.386	5
5	219	3
5	48.184	5
4	200	3
4	40.204	5
3	20	2
3	424	3
2	1	1
2	6	1
1	0	1
1	4	1

	[QM5] Case X = 5
One can find the regular numbers of the form n²+(n+5) at %N n^2 + (n+5). under A027690. The palindromic numbers of the form n²+(n+5) are categorised as follows : %N n^2 + (n+5) is a palindrome. under A027718. %N Palindromes of the form n^2 + (n+5). under A027728. More terms from Giovanni Resta, Aug 28, 2018. See Index Nrs 30 up to 46. More terms from Patrick De Geest, Sep 1, 2020. See Index Nrs 47 up to 79. More terms from Robert Xiao, Nov 11, 2022. See Index Nrs 80 up to 87. More terms from Robert Xiao, Dec 6, 2022. See Index Nrs 88 up to 94. More terms from Robert Xiao, Jul 18, 2023. See Index Nrs 95 up to 97.
97	2.741.097.489.407.795.894.534.146.448	28
97	7.513.615.446.437.721.726.230.412.801.082.140.326.271.277.346.445.163.157	55
96	2.321.583.477.758.376.828.874.021.805	28
96	5.389.749.844.200.679.760.082.306.490.946.032.800.679.760.024.489.479.835	55
95	2.312.974.744.804.653.668.859.324.594	28
95	5.349.852.170.104.152.764.124.581.678.761.854.214.672.514.010.712.589.435	55
94	7.724.893.520.176.131.722.830.409	25
94	59.673.979.898.059.188.008.749.155.194.780.088.195.089.897.937.695	50
93	7.168.715.561.822.749.647.862.085	25
93	51.390.482.806.319.661.128.549.322.394.582.116.691.360.828.409.315	50
92	276.930.549.956.726.857.275.578	24
92	76.690.529.499.335.189.572.067.476.027.598.153.399.492.509.667	47
91	231.039.377.440.567.687.892.430	24
91	53.379.193.928.125.097.468.095.059.086.479.052.182.939.197.335	47
90	34.440.033.402.705.514.519.042	23
90	1.186.115.900.779.471.580.807.337.080.851.749.770.095.116.811	46
89	23.148.775.498.877.278.516.494	23
89	535.865.807.097.420.994.859.868.958.499.024.790.708.568.535	45
88	10.657.437.381.077.853.690.857	23
88	113.580.971.531.595.580.831.393.138.085.595.135.179.085.311	45
87	8.773.059.802.826.288.434.478	22
87	76.966.578.303.966.434.903.444.430.943.466.930.387.566.967	44
86	2.817.140.814.595.263.786.456	22
86	7.936.282.369.258.466.412.199.912.146.648.529.632.826.397	43
85	2.701.333.536.188.917.348.558	22
85	7.297.202.873.738.920.834.422.244.380.298.373.782.027.927	43
84	1.094.835.918.541.132.095.737	22
84	1.198.665.688.527.804.433.884.883.344.087.258.865.668.911	43
83	1.049.185.679.191.036.040.877	22
83	1.100.790.589.419.555.597.559.557.955.559.149.850.970.011	43
82	233.630.688.688.326.669.315	21
82	54.583.298.696.981.811.115.651.111.818.969.689.238.545	41
81	128.666.957.189.116.742.292	21
81	16.555.185.872.306.000.532.823.500.060.327.858.155.561	41
80	12.655.405.880.861.430.032	20
80	Prime! 160.159.298.009.342.067.797.760.243.900.892.951.061	39
79	3.438.846.839.357.135.357	19
79	11.825.667.584.556.559.511.595.565.548.576.652.811	38
78	2.821.048.328.990.795.231	19
78	7.958.313.674.501.758.047.408.571.054.763.138.597	37
77	2.808.651.171.354.901.886	19
77	7.888.521.402.353.262.439.342.623.532.041.258.887	37
76	2.662.636.067.713.063.398	19
76	7.089.630.829.086.485.135.315.846.809.280.369.807	37
75	Prime! 1.266.537.051.930.343.607	19
75	1.604.116.103.912.405.899.985.042.193.016.114.061	37
74	1.092.269.214.303.220.062	19
74	1.193.052.036.514.573.674.763.754.156.302.503.911	37
73	1.065.112.309.613.110.542	19
73	1.134.464.232.089.374.652.564.739.802.324.644.311	37
72	854.071.216.890.041.433	18
72	729.437.643.520.036.195.591.630.025.346.734.927	36
71	710.487.567.770.103.224	18
71	504.792.583.955.877.022.220.778.559.385.297.405	36
70	272.740.912.616.759.106	18
70	74.387.605.415.022.626.762.622.051.450.678.347	35
69	128.516.445.113.554.267	18
69	16.516.476.664.625.206.560.252.646.667.461.561	35
68	127.555.335.548.680.952	18
68	16.270.363.626.936.590.709.563.962.636.307.261	35
67	127.325.246.849.329.752	18
67	16.211.718.485.242.756.065.724.258.481.711.261	35
66	73.856.398.697.590.940	17
66	5.454.767.628.577.512.772.157.758.267.674.545	34
65	28.182.867.034.430.531	17
65	794.273.994.280.391.181.193.082.499.372.497	33
64	24.124.980.160.964.119	17
64	582.014.667.766.912.353.219.667.766.410.285	33
63	10.891.052.175.305.917	17
63	118.615.017.485.235.757.532.584.710.516.811	33
62	10.742.267.540.559.297	17
62	115.396.311.912.953.898.359.219.113.693.511	33
61	7.649.794.162.480.819	16
61	58.519.350.728.325.622.652.382.705.391.585	32
60	7.200.217.655.047.414	16
60	51.843.134.280.056.488.465.008.243.134.815	32
59	Prime! 2.709.031.479.580.963	16
59	7.338.851.557.360.624.260.637.551.588.337	31
58	2.689.612.932.909.633	16
58	7.234.017.728.874.760.674.788.277.104.327	31
57	2.391.927.132.618.754	16
57	5.721.315.407.757.776.777.577.045.131.275	31
56	1.274.252.737.050.152	16
56	1.623.720.037.879.805.089.787.300.273.261	31
55	709.962.501.910.224	15
55	504.046.754.118.625.526.811.457.640.405	30
54	266.915.367.273.771	15
54	71.243.813.286.892.329.868.231.834.217	29
53	264.586.807.048.126	15
53	70.006.178.463.922.522.936.487.160.007	29
52	128.523.687.718.107	15
52	16.518.338.304.661.616.640.383.381.561	29
51	127.307.298.113.552	15
51	16.207.148.152.972.927.925.184.170.261	29
50	107.441.307.275.097	15
50	11.543.634.508.981.918.980.543.634.511	29
49	106.650.062.701.657	15
49	11.374.235.874.267.476.247.853.247.311	29
48	104.926.659.615.122	15
48	Prime! 11.009.603.897.987.778.979.830.690.011	29
47	10.685.559.255.237	14
47	114.181.176.597.191.795.671.181.411	27
46	2.724.617.501.718	13
46	7.423.540.530.670.760.350.453.247	25
45	2.413.553.760.255	13
45	5.825.241.753.643.463.571.425.285	25
44	1.274.687.352.352	13
44	1.624.827.846.247.426.487.284.261	25
43	1.092.675.882.737	13
43	1.193.940.584.716.174.850.493.911	25
42	712.311.093.700	12
42	507.387.094.208.802.490.783.705	24
41	128.760.203.492	12
41	16.579.190.003.430.009.197.561	23
40	127.651.865.352	12
40	16.294.998.727.972.789.949.261	23
39	87.304.087.378	11
39	7.622.003.672.992.763.002.267	22
38	84.526.784.828	11
38	7.144.777.353.443.537.774.417	22
37	27.413.239.448	11
37	751.485.697.060.796.584.157	21
36	24.070.821.945	11
36	579.404.469.131.964.404.975	21
35	23.203.983.194	11
35	538.424.836.090.638.424.835	21
34	4.029.203.527	10
34	16.234.481.066.018.443.261	20
33	2.815.069.131	10
33	7.924.614.215.124.164.297	19
32	2.781.875.716	10
32	Prime! 7.738.832.502.052.388.377	19
31	2.765.569.146	10
31	7.648.372.704.072.738.467	19
30	2.426.472.519	10
30	5.887.768.887.888.677.885	19
29	2.237.334.999	10
29	5.005.667.899.987.665.005	19
28	Prime! 106.617.617	9
28	11.367.316.361.376.311	17
27	87.579.753	8
27	7.670.213.223.120.767	16
26	85.125.933	8
26	7.246.424.554.246.427	16
25	7.569.245	7
25	57.293.477.439.275	14
24	4.063.892	7
24	16.515.222.251.561	14
23	2.775.383	7
23	7.702.753.572.077	13
22	2.724.718	7
22	Prime! 7.424.090.904.247	13
21	2.358.150	7
21	5.560.873.780.655	13
20	107.422	6
20	11.539.593.511	11
19	105.322	6
19	11.092.829.011	11
18	28.168	5
18	793.464.397	9
17	27.548	5
17	758.919.857	9
16	22.424	5
16	502.858.205	9
15	12.752	5
15	162.626.261	9
14	4.067	4
14	16.544.561	8
13	4.012	4
13	16.100.161	8
12	3.462	4
12	11.988.911	8
11	2.751	4
11	7.570.757	7
10	230	3
10	53.135	5
9	224	3
9	50.405	5
8	Prime! 127	3
8	16.261	5
7	74	2
7	5.555	4
6	26	2
6	707	3
5	12	2
5	161	3
4	8	1
4	77	2
3	Prime! 2	1
3	Prime! 11	2
2	1	1
2	Prime! 7	1
1	0	1
1	Prime! 5	1

	[QM6] Case X = 6
One can find the regular numbers of the form n²+(n+6) at %N n^2 + (n+6). under A027691. The palindromic numbers of the form n²+(n+6) are categorised as follows : %N n^2 + (n+6) is a palindrome. under A027729. %N Palindromes of the form n^2 + (n+6). under A027721. More terms from Giovanni Resta, Aug 27, 2018. See Index Nrs 32 up to 34. More terms from Patrick De Geest, Sep 1, 2020. See Index Nrs 35 up to 54. More terms from Robert Xiao, Nov 11, 2022. See Index Nrs 55 up to 63. More terms from Robert Xiao, Dec 6, 2022. See Index Nrs 64 up to 75. More terms from Patrick De Geest, Jun 22, 2023. See Index Nrs 76 up to 78. More terms from Patrick De Geest, Jul 18, 2023. See Index Nr 79.
79	2.874.297.145.398.462.335.096.954.658	28
79	8.261.584.080.045.749.329.477.192.378.732.917.749.239.475.400.804.851.628	55
78	283.829.342.698.845.400.785.348.373	27
78	80.559.095.776.858.625.017.648.318.381.384.671.052.685.867.759.095.508	53
77	Prime! 147.801.308.817.066.431.064.004.717	27
77	21.845.226.888.037.839.135.901.010.701.010.953.193.873.088.862.254.812	53
76	146.510.768.911.536.844.179.295.762	27
76	21.465.405.407.049.751.032.909.322.022.390.923.015.794.070.450.456.412	53
75	28.808.030.648.133.248.701.533.566	26
75	829.902.629.823.784.565.259.188.131.881.952.565.487.328.926.209.928	51
74	25.498.075.419.925.390.458.470.425	26
74	650.151.850.120.203.376.966.060.141.060.669.673.302.021.058.151.056	51
73	25.244.234.944.717.175.068.503.830	26
73	637.271.397.944.079.754.987.094.323.490.789.457.970.449.793.172.736	51
72	14.783.442.152.732.972.665.836.442	26
72	218.550.161.883.202.109.113.317.797.713.311.901.202.388.161.055.812	51
71	2.615.815.820.738.709.802.614.544	25
71	6.842.492.408.026.929.976.682.097.902.866.799.296.208.042.942.486	49
70	2.570.320.002.048.220.603.364.460	25
70	6.606.544.912.929.164.766.674.687.864.766.674.619.292.194.456.066	49
69	1.469.399.355.246.223.578.086.222	25
69	2.159.134.465.198.017.558.712.001.002.178.557.108.915.644.319.512	49
68	1.460.737.055.811.722.509.118.057	25
68	2.133.752.746.221.499.320.551.537.351.550.239.941.226.472.573.312	49
67	292.438.232.461.254.812.293.351	24
67	85.520.119.805.062.907.829.875.157.892.870.926.050.891.102.558	47
66	260.165.118.520.509.050.834.229	24
66	67.685.888.894.790.521.531.640.304.613.512.509.749.888.858.676	47
65	147.893.672.859.830.109.963.482	24
65	21.872.538.471.970.449.256.634.243.665.294.407.917.483.527.812	47
64	28.985.874.843.495.529.237.006	23
64	840.180.940.442.786.971.539.080.935.179.687.244.049.081.048	45
63	2.987.335.598.947.757.919.131	22
63	8.924.173.980.740.559.545.114.115.459.550.470.893.714.298	43
62	1.615.639.009.407.151.056.787	22
62	2.610.289.408.718.120.340.968.690.430.218.178.049.820.162	43
61	296.053.623.414.021.923.183	21
61	87.647.747.936.571.509.891.219.890.517.563.974.774.678	41
60	293.185.592.806.891.151.151	21
60	85.957.791.829.528.184.310.901.348.182.592.819.775.958	41
59	286.353.194.167.746.026.328	21
59	81.998.151.810.070.856.868.086.865.807.001.815.189.918	41
58	259.892.958.171.568.404.329	21
58	67.544.349.707.168.604.230.503.240.686.170.794.344.576	41
57	254.235.549.230.472.251.415	21
57	64.635.714.492.519.879.788.888.797.891.529.441.753.646	41
56	163.435.381.459.705.732.227	21
56	26.711.123.912.879.524.200.300.242.597.821.932.111.762	41
55	14.794.168.948.789.166.882	20
55	218.867.434.885.317.563.080.365.713.588.434.768.812	39
54	2.985.831.125.619.083.431	19
54	8.915.187.510.715.722.782.872.275.170.157.815.198	37
53	2.916.855.303.079.661.851	19
53	8.508.044.859.103.945.996.995.493.019.584.408.058	37
52	2.551.552.617.878.235.474	19
52	6.510.420.761.801.276.736.376.721.081.670.240.156	37
51	1.463.508.671.957.677.637	19
51	2.141.857.632.895.325.294.925.235.982.367.581.412	37
50	254.045.687.862.089.940	18
50	64.539.211.521.322.432.123.422.312.511.293.546	35
49	162.090.760.203.886.327	18
49	26.273.414.543.473.779.597.737.434.541.437.262	35
48	147.870.657.622.296.957	18
48	21.865.731.385.650.569.296.505.658.313.756.812	35
47	29.498.083.994.743.008	17
47	870.136.959.360.913.646.319.063.959.631.078	33
46	14.500.619.401.279.597	17
46	210.267.963.020.766.272.667.020.369.762.012	33
45	287.460.767.600.658	15
45	82.633.692.909.559.795.590.929.633.628	29
44	255.814.556.383.825	15
44	65.441.087.257.853.435.875.278.014.456	29
43	162.126.124.865.152	15
43	26.284.880.363.791.019.736.308.848.262	29
42	26.199.714.854.344	14
42	686.425.058.448.959.844.850.524.686	27
41	2.610.993.061.219	13
41	6.817.284.765.736.375.674.827.186	25
40	2.565.389.200.649	13
40	6.581.221.750.809.080.571.221.856	25
39	2.497.478.799.079	13
39	6.237.400.351.851.581.530.047.326	25
38	1.630.700.084.692	13
38	2.659.182.766.216.126.672.819.562	25
37	1.614.498.398.967	13
37	2.606.605.080.268.620.805.066.062	25
36	293.212.995.776	12
36	85.973.860.892.229.806.837.958	23
35	286.306.469.671	12
35	81.971.394.575.757.549.317.918	23
34	29.959.390.368	11
34	897.565.071.252.170.565.798	21
33	28.988.127.118	11
33	840.311.513.838.315.113.048	21
32	2.931.604.151	10
32	8.594.302.901.092.034.958	19
31	2.853.889.203	10
31	8.144.683.585.853.864.418	19
30	288.888.888	9
30	83.456.789.898.765.438	17
29	264.056.434	9
29	69.725.800.600.852.796	17
28	148.278.137	9
28	21.986.406.060.468.912	17
27	29.585.508	8
27	875.302.313.203.578	15
26	29.190.748	8
26	852.099.797.990.258	15
25	28.888.888	8
25	834.567.878.765.438	15
24	16.353.547	8
24	267.438.515.834.762	15
23	14.604.657	8
23	213.296.020.692.312	15
22	2.995.631	7
22	8.973.808.083.798	13
21	Prime! 2.985.943	7
21	8.915.858.585.198	13
20	2.960.816	7
20	8.766.434.346.678	13
19	2.952.316	7
19	8.716.172.716.178	13
18	2.888.888	7
18	8.345.676.765.438	13
17	2.873.233	7
17	8.255.470.745.528	13
16	Prime! 2.834.101	7
16	8.032.131.312.308	13
15	292.276	6
15	85.425.552.458	11
14	288.888	6
14	83.456.565.438	11
13	264.334	6
13	69.872.727.896	11
12	Prime! 146.777	6
12	21.543.634.512	11
11	28.888	5
11	834.545.438	9
10	2.946	4
10	8.681.868	7
9	2.888	4
9	8.343.438	7
8	2.550	4
8	6.505.056	7
7	2.485	4
7	6.177.716	7
6	288	3
6	83.238	5
5	28	2
5	818	3
4	25	2
4	656	3
3	24	2
3	606	3
2	1	1
2	8	1
1	0	1
1	6	1

	[QM7] Case X = 7
One can find the regular numbers of the form n²+(n+7) at %N n^2 + (n+7). under A027692. The palindromic numbers of the form n²+(n+7) are categorised as follows : %N n^2 + (n+7) is a palindrome. under A027722. %N Palindromes of the form n^2 + (n+7). under A027723. More terms from Giovanni Resta, Aug 28, 2018. See Index Nrs 28 up to 45. More terms from Patrick De Geest, Sep 1, 2020. See Index Nrs 46 up to 71. More terms from Robert Xiao, Nov 11, 2022. See Index Nrs 72 up to 80. More terms from Robert Xiao, Dec 6, 2022. See Index Nrs 81 up to 96. More terms from Patrick De Geest, Jun 22, 2023. See Index Nrs 97 up to 99. More terms from Patrick De Geest, Jul 18, 2023. See Index Nrs 100 up to 103.
103	3.121.000.000.000.000.000.000.001.208	28
103	9.740.641.000.000.000.000.000.007.543.457.000.000.000.000.000.001.460.479	55
102	3.000.000.000.000.000.000.000.000.001	28
102	9.000.000.000.000.000.000.000.000.009.000.000.000.000.000.000.000.000.009	55
101	2.821.774.784.748.357.549.523.525.409	28
101	7.962.412.935.841.639.581.883.069.452.549.603.881.859.361.485.392.142.697	55
100	2.772.985.384.440.605.266.228.026.635	28
100	7.689.447.942.321.211.382.921.626.343.436.261.292.831.121.232.497.449.867	55
99	315.379.187.639.614.006.145.294.156	27
99	99.464.031.996.222.859.912.937.826.762.873.921.995.822.269.913.046.499	53
98	312.100.000.000.000.000.000.001.208	27
98	97.406.410.000.000.000.000.000.754.345.700.000.000.000.000.001.460.479	53
97	300.000.000.000.000.000.000.000.001	27
97	90.000.000.000.000.000.000.000.000.900.000.000.000.000.000.000.000.009	53
96	31.210.000.000.000.000.000.001.208	26
96	974.064.100.000.000.000.000.075.434.570.000.000.000.000.001.460.479	51
95	30.000.000.000.000.000.000.000.001	26
95	900.000.000.000.000.000.000.000.090.000.000.000.000.000.000.000.009	51
94	3.121.000.000.000.000.000.001.208	25
94	9.740.641.000.000.000.000.007.543.457.000.000.000.000.001.460.479	49
93	3.100.357.559.888.528.326.840.046	25
93	9.612.216.999.157.949.510.797.804.087.970.159.497.519.996.122.169	49
92	3.082.675.293.024.238.368.864.523	25
92	9.502.886.962.222.073.890.683.161.613.860.983.702.222.696.882.059	49
91	3.000.000.000.000.000.000.000.001	25
91	9.000.000.000.000.000.000.000.009.000.000.000.000.000.000.000.009	49
90	2.654.409.154.426.579.861.084.775	25
90	7.045.887.959.103.630.692.532.923.292.352.960.363.019.597.885.407	49
89	1.916.823.575.746.489.052.351.172	25
89	3.674.212.620.537.556.253.609.519.159.063.526.557.350.262.124.763	49
88	312.100.000.000.000.000.001.208	24
88	97.406.410.000.000.000.000.754.345.700.000.000.000.001.460.479	47
87	300.000.000.000.000.000.000.001	24
87	90.000.000.000.000.000.000.000.900.000.000.000.000.000.000.009	47
86	177.682.217.094.375.865.696.622	24
86	31.570.970.271.572.915.105.447.074.450.151.927.517.207.907.513	47
85	176.938.468.365.190.722.850.142	24
85	31.307.221.587.419.598.191.197.879.119.189.591.478.512.270.313	47
84	31.210.000.000.000.000.001.208	23
84	974.064.100.000.000.000.075.434.570.000.000.000.001.460.479	45
83	30.616.010.059.832.974.528.836	23
83	937.340.071.983.793.896.589.191.985.698.397.389.170.043.739	45
82	30.000.000.000.000.000.000.001	23
82	900.000.000.000.000.000.000.090.000.000.000.000.000.000.009	45
81	27.680.644.579.504.590.686.564	23
81	766.218.084.336.856.878.146.585.641.878.658.633.480.812.667	45
80	3.121.000.000.000.000.001.208	22
80	9.740.641.000.000.000.007.543.457.000.000.000.001.460.479	43
79	3.000.000.000.000.000.000.001	22
79	9.000.000.000.000.000.000.009.000.000.000.000.000.000.009	43
78	312.100.000.000.000.001.208	21
78	97.406.410.000.000.000.754.345.700.000.000.001.460.479	41
77	300.000.000.000.000.000.001	21
77	90.000.000.000.000.000.000.900.000.000.000.000.000.009	41
76	31.506.730.336.917.391.243	20
76	992.674.056.523.230.669.939.966.032.325.650.476.299	39
75	31.210.000.000.000.001.208	20
75	974.064.100.000.000.075.434.570.000.000.001.460.479	39
74	31.195.432.792.677.686.716	20
74	973.155.027.122.470.376.101.673.074.221.720.551.379	39
73	30.000.000.000.000.000.001	20
73	900.000.000.000.000.000.090.000.000.000.000.000.009	39
72	27.622.856.194.472.462.135	20
72	763.022.184.340.505.672.888.276.505.043.481.220.367	39
71	3.121.000.000.000.001.208	19
71	9.740.641.000.000.007.543.457.000.000.001.460.479	37
70	3.021.993.199.130.681.096	19
70	9.132.442.895.592.088.370.738.802.955.982.442.319	37
69	3.000.000.000.000.000.001	19
69	9.000.000.000.000.000.009.000.000.000.000.000.009	37
68	2.722.509.353.145.589.459	19
68	7.412.057.177.965.215.939.395.125.697.717.502.147	37
67	1.915.035.496.742.374.887	19
67	3.667.360.953.783.314.538.354.133.873.590.637.663	37
66	312.100.000.000.001.208	18
66	97.406.410.000.000.754.345.700.000.001.460.479	35
65	300.000.000.000.000.001	18
65	90.000.000.000.000.000.900.000.000.000.000.009	35
64	277.182.107.823.074.739	18
64	76.829.920.897.242.630.703.624.279.802.992.867	35
63	191.130.616.729.367.092	18
63	36.530.912.651.348.219.891.284.315.621.903.563	35
62	31.210.000.000.001.208	17
62	974.064.100.000.075.434.570.000.001.460.479	33
61	30.648.097.516.689.388	17
61	939.305.881.392.502.262.205.293.188.503.939	33
60	30.000.000.000.000.001	17
60	900.000.000.000.000.090.000.000.000.000.009	33
59	19.124.750.677.376.132	17
59	365.756.088.471.798.838.897.174.880.657.563	33
58	3.137.955.834.553.086	16
58	9.846.766.819.605.757.575.069.186.676.489	31
57	3.121.000.000.001.208	16
57	9.740.641.000.007.543.457.000.001.460.479	31
56	3.083.258.898.592.148	16
56	9.506.485.435.747.668.667.475.345.846.059	31
55	3.000.000.000.000.001	16
55	9.000.000.000.000.009.000.000.000.000.009	31
54	2.702.530.723.613.869	16
54	7.303.672.312.076.905.096.702.132.763.037	31
53	312.100.000.001.208	15
53	97.406.410.000.754.345.700.001.460.479	29
52	300.000.000.000.001	15
52	90.000.000.000.000.900.000.000.000.009	29
51	268.792.508.783.804	15
51	72.249.412.778.291.619.287.721.494.227	29
50	264.773.198.830.100	15
50	70.104.846.818.723.932.781.864.840.107	29
49	177.377.074.711.837	15
49	31.462.626.633.328.782.333.662.626.413	29
48	31.210.000.001.208	14
48	974.064.100.075.434.570.001.460.479	27
47	30.000.000.000.001	14
47	900.000.000.000.090.000.000.000.009	27
46	17.615.399.751.397	14
46	310.302.308.401.535.104.803.203.013	27
45	3.149.974.520.756	13
45	9.922.339.481.415.141.849.332.299	25
44	3.121.000.001.208	13
44	9.740.641.007.543.457.001.460.479	25
43	3.041.875.952.766	13
43	9.253.009.312.019.102.139.003.529	25
42	3.000.000.000.001	13
42	9.000.000.000.009.000.000.000.009	25
41	2.702.976.653.994	13
41	7.306.082.792.039.302.972.806.037	25
40	1.900.006.888.012	13
40	3.610.026.174.494.944.716.200.163	25
39	312.100.001.208	12
39	97.406.410.754.345.701.460.479	23
38	300.000.000.001	12
38	90.000.000.000.900.000.000.009	23
37	281.757.625.709	12
37	79.387.359.645.454.695.378.397	23
36	275.313.182.749	12
36	75.797.348.595.659.584.379.757	23
35	266.584.070.214	12
35	71.067.066.492.129.466.076.017	23
34	31.210.001.208	11
34	974.064.175.434.571.460.479	21
33	31.006.644.078	11
33	Prime! 961.411.977.010.779.114.169	21
32	30.805.056.481	11
32	948.951.504.828.405.159.849	21
31	Prime! 30.000.000.001	11
31	900.000.000.090.000.000.009	21
30	28.255.878.334	11
30	798.394.660.454.066.493.897	21
29	26.928.832.879	11
29	725.162.040.252.040.261.527	21
28	3.121.001.208	10
28	9.740.648.543.458.460.479	19
27	3.000.000.001	10
27	9.000.000.009.000.000.009	19
26	2.817.818.390	10
26	7.940.100.481.840.010.497	19
25	2.673.533.185	10
25	7.147.779.693.969.777.417	19
24	303.758.458	9
24	92.269.201.110.296.229	17
23	300.000.001	9
23	90.000.000.900.000.009	17
22	30.122.098	8
22	907.340.818.043.709	15
21	Prime! 30.000.001	8
21	900.000.090.000.009	15
20	27.515.125	8
20	757.082.131.280.757	15
19	3.000.001	7
19	9.000.009.000.009	13
18	1.762.122	7
18	3.105.075.705.013	13
17	312.208	6
17	97.474.147.479	11
16	300.001	6
16	90.000.900.009	11
15	177.237	6
15	31.413.131.413	11
14	30.001	5
14	900.090.009	9
13	Prime! 27.259	5
13	743.080.347	9
12	Prime! 3.001	4
12	9.009.009	7
11	2.764	4
11	7.642.467	7
10	Prime! 1.777	4
10	3.159.513	7
9	Prime! 313	3
9	98.289	5
8	301	3
8	90.909	5
7	280	3
7	78.687	5
6	274	3
6	75.357	5
5	177	3
5	Prime! 31.513	5
4	Prime! 31	2
4	999	3
3	Prime! 17	2
3	Prime! 313	3
2	1	1
2	9	1
1	0	1
1	Prime! 7	1

	[QM8] Case X = 8
One can find the regular numbers of the form n²+(n+8) at %N n^2 + (n+8). under A027693. The palindromic numbers of the form n²+(n+8) are categorised as follows : %N n^2 + (n+8) is a palindrome. under A027724. %N Palindromes of the form n^2 + (n+8). under A027725. More terms from Giovanni Resta, Aug 29, 2018. See Index Nrs 16 up to 19. More terms from Patrick De Geest, Sep 1, 2020. See Index Nrs 20 up to 32. More terms from Robert Xiao, Nov 11, 2022. See Index Nrs 33 up to 41. More terms from Robert Xiao, Dec 6, 2022. See Index Nrs 42 up to 45. More terms from Patrick De Geest, Jun 22, 2023. See Index Nr 46. More terms from Patrick De Geest, Jul 18, 2023. See Index Nr 47.
47	2.024.980.892.661.756.697.013.490.002	28
47	4.100.547.615.645.204.997.648.623.368.633.268.467.994.025.465.167.450.014	55
46	291.110.773.714.896.523.959.619.515	27
46	84.745.482.572.885.688.920.872.755.855.727.802.988.658.827.528.454.748	53
45	28.871.285.875.858.590.001.229.569	26
45	833.551.148.125.551.710.375.568.181.865.573.017.155.521.841.155.338	51
44	21.483.563.234.526.184.866.880.587	26
44	461.543.489.251.885.190.477.082.818.280.774.091.588.152.984.345.164	51
43	2.928.331.740.489.196.140.653.250	25
43	8.575.126.782.356.484.771.760.148.410.671.774.846.532.876.215.758	49
42	2.159.210.693.397.915.883.253.487	25
42	4.662.190.818.483.908.709.229.276.729.229.078.093.848.180.912.664	49
41	2.958.418.939.805.275.953.670	22
41	8.752.242.623.398.572.986.568.656.892.758.933.262.422.578	43
40	2.855.744.435.294.488.382.589	22
40	8.155.276.279.715.436.344.590.954.436.345.179.726.725.518	43
39	2.146.566.864.566.595.055.807	22
39	46.076.865.807.219.121.234.843.212.191.270.856.867.064	43
38	214.655.225.436.557.032.432	21
38	46.076.865.807.219.121.234.843.212.191.270.856.867.064	41
37	29.927.294.176.812.473.509	20
37	895.642.936.745.473.786.434.687.374.547.639.246.598	39
36	29.201.685.813.894.053.374	20
36	852.738.454.373.381.202.454.202.183.373.454.837.258	39
35	28.627.570.794.205.246.685	20
35	819.537.809.577.233.218.474.812.332.775.908.735.918	39
34	21.453.822.714.860.484.567	20
34	460.266.509.080.663.692.515.296.366.080.905.662.064	39
33	20.362.349.579.179.647.037	20
33	414.625.280.384.717.548.797.845.717.483.082.526.414	39
32	2.919.019.406.760.380.374	19
32	8.520.674.297.043.722.974.792.273.407.924.760.258	37
31	2.896.827.497.610.422.905	19
31	8.391.609.550.911.864.724.274.681.190.559.061.938	37
30	204.899.512.505.754.537	18
30	41.983.810.225.095.860.106.859.052.201.838.914	35
29	29.293.314.111.168.350	17
29	858.098.251.615.574.808.475.516.152.890.858	33
28	28.989.019.759.841.184	17
28	840.363.266.636.462.646.264.636.662.363.048	33
27	21.622.406.372.184.972	17
27	467.528.457.323.905.303.509.323.754.825.764	33
26	21.459.803.444.244.992	17
26	460.523.163.865.629.242.926.568.361.325.064	33
25	2.989.063.335.060.290	16
25	8.934.499.621.001.746.471.001.269.944.398	31
24	2.930.792.062.562.649	16
24	8.589.542.113.980.229.220.893.112.459.858	31
23	Prime! 2.927.399.306.452.849	16
23	8.569.666.699.420.624.260.249.966.669.658	31
22	2.162.277.851.899.027	16
22	4.675.445.508.813.072.703.188.055.445.764	31
21	288.191.799.404.994	15
21	83.054.513.244.288.588.244.231.545.038	29
20	286.006.098.215.514	15
20	81.799.488.216.462.526.461.288.499.718	29
19	21.614.586.653.852	14
19	467.190.356.216.898.612.653.091.764	27
18	21.495.814.697.072	14
18	462.070.049.490.878.094.940.070.264	27
17	295.431.039.629	12
17	87.279.499.176.567.199.497.278	23
16	202.542.945.597	12
16	41.023.644.811.311.844.632.014	23
15	2.926.428.849	10
15	8.563.985.811.185.893.658	19
14	287.010.920	9
14	82.375.268.486.257.328	17
13	2.997.334	7
13	8.984.014.104.898	13
12	2.990.390	7
12	8.942.435.342.498	13
11	2.837.875	7
11	8.053.537.353.508	13
10	2.834.699	7
10	8.035.521.255.308	13
9	297.119	6
9	88.279.997.288	11
8	29.570	5
8	874.414.478	9
7	20.377	5
7	415.242.514	9
6	2.935	4
6	8.617.168	7
5	2.925	4
5	8.558.558	7
4	285	3
4	81.518	5
3	202	3
3	41.014	5
2	Prime! 29	2
2	878	3
1	0	1
1	8	1

	[QM9] Case X = 9
One can find the regular numbers of the form n²+(n+9) at %N n^2 + (n+9). under A027694. The palindromic numbers of the form n²+(n+9) are categorised as follows : %N n^2 + (n+9) is a palindrome. under A027726. %N Palindromes of the form n^2 + (n+9). under A027727. More terms from Giovanni Resta, Aug 29, 2018. From Index Nrs 64 up to 71. More terms from Patrick De Geest, Sep 1, 2020. See Index Nrs 72 up to 117. More terms from Robert Xiao, Nov 11, 2022. See Index Nrs 118 up to 139. More terms from Robert Xiao, Dec 6, 2022. See Index Nrs 140 up to 164. More terms from Patrick De Geest, Jun 22, 2023. See Index Nr 165. More terms from Patrick De Geest, Jul 18, 2023. See Index Nrs 166 up to 170.
170	3.000.000.000.000.000.000.000.000.000	28
170	9.000.000.000.000.000.000.000.000.003.000.000.000.000.000.000.000.000.009	55
169	1.300.626.441.328.197.235.814.996.223	28
169	1.691.629.139.882.050.486.635.905.970.795.095.366.840.502.889.319.261.961	55
168	1.212.047.305.612.471.054.938.423.488	28
168	1.469.058.671.042.450.808.432.367.053.507.632.348.080.542.401.768.509.641	55
167	1.038.115.544.834.502.662.675.766.556	28
167	1.077.683.884.427.036.307.962.598.482.848.952.697.036.307.244.883.867.701	55
166	445.552.612.841.909.255.019.167.238	27
166	198.517.130.810.252.279.990.339.340.043.933.099.972.252.018.031.715.891	54
165	300.000.000.000.000.000.000.000.000	27
165	90.000.000.000.000.000.000.000.000.300.000.000.000.000.000.000.000.009	53
164	41.258.286.155.045.197.995.785.653	26
164	1.702.246.176.451.594.267.712.515.995.152.177.624.951.546.716.422.071	52
163	31.299.788.623.815.043.712.792.070	26
163	979.676.767.895.501.627.987.458.151.854.789.726.105.598.767.676.979	51
162	30.000.000.000.000.000.000.000.000	26
162	900.000.000.000.000.000.000.000.030.000.000.000.000.000.000.000.009	51
161	23.815.774.266.794.138.373.708.227	26
161	567.191.103.926.893.879.245.037.646.730.542.978.398.629.301.191.765	51
160	23.712.230.028.151.813.684.241.327	26
160	562.269.852.907.984.562.788.280.080.082.887.265.489.709.258.962.265	51
159	12.394.706.146.927.753.774.755.106	26
159	153.628.740.468.688.644.144.724.363.427.441.446.886.864.047.826.351	51
158	9.643.512.104.845.529.156.149.520	25
158	92.997.325.716.302.248.119.940.533.504.991.184.220.361.752.379.929	50
157	4.431.825.874.452.201.960.213.513	25
157	19.641.080.581.464.024.571.300.022.000.317.542.046.418.508.014.691	50
156	3.264.045.264.937.547.813.954.856	25
156	10.653.991.491.561.226.700.704.800.840.700.762.216.519.419.935.601	50
155	3.113.886.626.232.284.537.657.360	25
155	9.696.289.921.028.279.306.529.652.569.256.039.728.201.299.826.969	49
154	3.000.000.000.000.000.000.000.000	25
154	9.000.000.000.000.000.000.000.003.000.000.000.000.000.000.000.009	49
153	1.066.398.967.008.718.874.807.773	25
153	1.137.206.756.837.262.687.176.899.986.717.862.627.386.576.027.311	49
152	1.057.045.827.943.140.327.018.826	25
152	1.117.345.882.371.999.023.790.845.480.973.209.991.732.885.437.111	49
151	1.030.672.161.696.389.924.736.768	25
151	1.062.285.104.895.909.338.739.104.019.378.339.095.984.015.822.601	49
150	364.999.234.483.451.745.508.241	24
150	133.224.441.173.505.789.806.667.766.608.987.505.371.144.422.331	48
149	305.089.298.522.463.407.227.005	24
149	93.079.480.072.928.792.556.118.481.165.529.782.927.008.497.039	47
148	300.000.000.000.000.000.000.000	24
148	90.000.000.000.000.000.000.000.300.000.000.000.000.000.000.009	47
147	128.827.237.225.970.387.982.351	24
147	16.596.457.051.276.450.506.231.313.260.505.467.215.075.469.561	47
146	127.462.410.833.734.378.632.876	24
146	16.246.666.175.547.687.095.910.901.959.078.674.557.166.664.261	47
145	123.465.885.738.164.872.614.718	24
145	15.243.824.941.109.584.091.464.346.419.048.590.114.942.834.251	47
144	71.423.065.283.032.760.286.922	23
144	5.101.254.254.424.359.550.312.112.130.559.534.244.524.521.015	46
143	40.316.744.034.191.202.094.251	23
143	1.625.439.849.518.491.884.941.441.494.881.948.159.489.345.261	46
142	31.916.093.660.165.724.742.643	23
142	1.018.637.034.524.470.768.416.006.148.670.744.254.307.368.101	46
141	30.000.000.000.000.000.000.000	23
141	900.000.000.000.000.000.000.030.000.000.000.000.000.000.009	45
140	14.066.088.021.782.561.085.061	23
140	197.854.832.236.534.842.650.181.056.248.435.632.238.458.791	45
139	9.836.061.969.333.312.238.535	22
139	96.748.115.064.565.116.627.633.672.661.156.546.051.184.769	44
138	3.364.568.676.278.731.164.101	22
138	11.320.322.377.396.013.263.599.536.231.069.377.322.302.311	44
137	3.049.721.756.523.937.483.130	22
137	9.300.802.792.215.450.618.448.448.160.545.122.972.080.039	43
136	3.000.000.000.000.000.000.000	22
136	9.000.000.000.000.000.000.003.000.000.000.000.000.000.009	43
135	2.271.420.430.650.818.082.222	22
135	5.159.350.772.777.947.876.770.776.787.497.772.770.539.515	43
134	1.379.288.397.736.143.707.838	22
134	1.902.436.484.129.538.559.034.309.558.359.214.846.342.091	43
133	1.200.078.014.948.814.916.736	22
133	1.440.187.241.963.488.038.761.678.308.843.691.427.810.441	43
132	1.074.517.913.653.292.201.501	22
132	1.154.588.746.761.823.915.299.925.193.281.676.478.854.511	43
131	997.379.892.715.904.184.609	21
131	994.766.650.393.988.541.168.861.145.889.393.056.667.499	42
130	394.175.206.747.692.290.493	21
130	155.374.093.614.585.961.818.818.169.585.416.390.473.551	42
129	300.000.000.000.000.000.000	21
129	90.000.000.000.000.000.000.300.000.000.000.000.000.009	41
128	237.820.296.677.998.624.667	21
128	56.558.493.512.011.283.671.717.638.211.021.539.485.565	41
127	237.726.197.335.200.876.267	21
127	56.513.744.899.454.868.204.640.286.845.499.844.731.565	41
126	227.673.388.532.799.324.117	21
126	51.835.171.846.006.998.775.757.789.960.064.817.153.815	41
125	124.586.806.687.185.390.618	21
125	15.521.872.400.510.102.366.266.320.101.500.427.812.551	41
124	96.993.056.329.597.442.815	20
124	9.407.652.976.156.462.565.555.652.646.516.792.567.049	40
123	31.267.734.922.481.568.254	20
123	977.671.247.182.573.443.141.344.375.281.742.176.779	39
122	30.948.088.830.885.074.749	20
122	Prime! 957.784.202.284.353.512.838.215.353.482.202.487.759	39
121	30.886.706.212.236.486.274	20
121	953.988.620.641.007.953.111.359.700.146.026.889.359	39
120	30.000.000.000.000.000.000	20
120	900.000.000.000.000.000.030.000.000.000.000.000.009	39
119	22.761.453.140.953.328.317	20
119	518.083.749.087.814.135.252.531.418.780.947.380.815	39
118	12.356.255.930.003.019.281	20
118	152.677.060.607.734.778.929.877.437.706.060.776.251	39
117	9.520.691.133.001.233.975	19
117	90.643.559.650.008.320.288.202.380.005.695.534.609	38
116	3.897.012.554.826.686.293	19
116	15.186.706.852.476.816.644.661.867.425.860.768.151	38
115	3.422.795.298.433.113.901	19
115	11.715.527.654.975.829.255.292.857.945.672.551.711	38
114	3.069.325.912.785.429.984	19
114	9.420.761.558.896.112.951.592.116.988.551.670.249	37
113	3.027.632.478.680.776.510	19
113	9.166.558.425.962.702.631.362.072.695.248.556.619	37
112	3.000.000.000.000.000.000	19
112	9.000.000.000.000.000.003.000.000.000.000.000.009	37
111	2.383.224.109.158.209.827	19
111	5.679.757.154.472.942.831.382.492.744.517.579.765	37
110	1.407.464.140.369.542.238	19
110	1.980.955.306.426.174.497.944.716.246.035.590.891	37
109	1.390.255.830.520.081.738	19
109	1.932.811.274.295.082.238.322.805.924.721.182.391	37
108	1.158.845.561.992.536.066	19
108	1.342.923.036.549.796.751.576.979.456.303.292.431	37
107	1.085.720.773.447.473.973	19
107	1.178.789.597.895.381.106.011.835.987.959.878.711	37
106	968.166.647.234.714.830	18
106	937.346.656.817.708.749.947.807.718.656.643.739	36
105	403.850.324.398.604.048	18
105	163.095.084.516.857.724.427.758.615.480.590.361	36
104	300.000.000.000.000.000	18
104	90.000.000.000.000.000.300.000.000.000.000.009	35
103	136.883.299.310.520.483	18
103	18.737.037.630.133.537.473.533.103.673.073.781	35
102	100.101.032.507.332.343	18
102	10.020.216.709.034.006.560.043.090.761.202.001	35
101	31.159.467.620.387.045	17
101	970.912.422.385.948.727.849.583.224.219.079	33
100	30.000.000.000.000.000	17
100	900.000.000.000.000.030.000.000.000.000.009	33
99	22.788.502.426.511.662	17
99	519.315.842.843.127.929.721.348.248.513.915	33
98	13.718.360.536.465.216	17
98	188.193.415.808.446.222.644.808.514.391.881	33
97	11.731.882.304.045.041	17
97	137.637.062.395.965.191.569.593.260.736.731	33
96	11.578.846.113.932.066	17
96	134.069.677.330.119.717.911.033.776.960.431	33
95	3.262.179.310.062.143	16
95	10.641.813.850.997.522.579.905.831.814.601	32
94	3.000.000.000.000.000	16
94	9.000.000.000.000.003.000.000.000.000.009	31
93	1.411.031.348.053.413	16
93	1.991.009.465.189.433.349.815.649.001.991	31
92	1.361.700.097.732.883	16
92	1.854.227.156.165.744.475.616.517.224.581	31
91	1.325.889.400.817.846	16
91	1.757.982.703.201.108.011.023.072.897.571	31
90	1.006.850.261.673.268	16
90	1.013.747.449.431.529.251.349.447.473.101	31
89	951.322.744.355.124	15
89	905.014.963.927.365.563.729.369.410.509	30
88	370.656.884.454.041	15
88	137.386.525.993.176.671.399.525.683.731	30
87	302.985.210.998.585	15
87	91.800.038.083.857.375.838.083.000.819	29
86	300.207.281.032.100	15
86	90.124.411.584.686.568.648.511.442.109	29
85	300.000.000.000.000	15
85	90.000.000.000.000.300.000.000.000.009	29
84	41.989.656.355.546	14
84	1.763.131.240.856.886.580.421.313.671	28
83	41.944.248.388.153	14
83	1.759.319.972.847.117.482.799.139.571	28
82	30.000.000.000.000	14
82	900.000.000.000.030.000.000.000.009	27
81	14.016.755.641.638	14
81	196.469.438.717.404.717.834.964.691	27
80	12.977.693.492.548	14
80	168.420.528.386.535.683.825.024.861	27
79	12.389.095.521.106	14
79	153.489.687.831.101.138.786.984.351	27
78	11.270.747.729.271	14
78	127.029.754.376.878.673.457.920.721	27
77	Prime! 3.809.272.592.563	13
77	14.510.557.684.455.448.675.501.541	26
76	3.000.000.000.000	13
76	9.000.000.000.003.000.000.000.009	25
75	1.379.803.137.286	13
75	1.903.856.697.665.667.966.583.091	25
74	1.179.335.179.433	13
74	1.390.831.465.449.445.641.380.931	25
73	1.161.363.821.933	13
73	1.348.765.926.895.986.295.678.431	25
72	Prime! 720.082.209.317	12
72	518.518.388.175.571.883.815.815	24
71	300.000.000.000	12
71	90.000.000.000.300.000.000.009	23
70	226.596.191.582	12
70	51.345.834.039.693.043.854.315	23
69	225.969.524.077	12
69	51.062.225.811.811.852.226.015	23
68	107.716.960.201	12
68	11.602.943.515.051.534.920.611	23
67	30.000.000.000	11
67	900.000.000.030.000.000.009	21
66	11.950.115.336	11
66	142.805.256.555.652.508.241	21
65	11.430.454.733	11
65	130.655.295.414.592.556.031	21
64	Prime! 3.040.137.979	10
64	9.242.438.934.398.342.429	19
63	3.000.000.000	10
63	9.000.000.003.000.000.009	19
62	1.078.247.673	10
62	1.162.618.045.408.162.611	19
61	989.943.054	9
61	979.987.251.152.789.979	18
60	387.851.993	9
60	150.429.168.861.924.051	18
59	349.101.696	9
59	121.871.994.499.178.121	18
58	Prime! 346.313.573	9
58	119.933.091.190.339.911	18
57	337.310.898	9
57	113.778.642.246.877.311	18
56	302.382.689	9
56	91.435.290.909.253.419	17
55	300.000.000	9
55	90.000.000.300.000.009	17
54	128.536.648	9
54	16.521.670.007.612.561	17
53	120.588.436	9
53	14.541.571.017.514.541	17
52	109.666.003	9
52	12.026.632.323.662.021	17
51	98.066.439	8
51	9.617.026.556.207.169	16
50	Prime! 41.794.853	8
50	1.746.809.779.086.471	16
49	35.409.496	8
49	1.253.832.442.383.521	16
48	30.880.274	8
48	953.591.353.195.359	15
47	30.592.630	8
47	935.909.040.909.539	15
46	30.447.695	8
46	927.062.161.260.729	15
45	30.000.000	8
45	900.000.030.000.009	15
44	23.683.392	8
44	560.903.080.309.065	15
43	13.220.978	8
43	174.794.272.497.471	15
42	10.222.456	8
42	104.498.616.894.401	15
41	7.489.392	7
41	56.091.000.019.065	14
40	3.932.806	7
40	15.466.966.966.451	14
39	3.152.290	7
39	9.936.935.396.399	13
38	3.045.679	7
38	9.276.163.616.729	13
37	3.040.604	7
37	9.245.275.725.429	13
36	3.000.000	7
36	9.000.003.000.009	13
35	Prime! 2.378.507	7
35	5.657.297.927.565	13
34	989.154	6
34	978.426.624.879	12
33	980.560	6
33	961.498.894.169	12
32	963.304	6
32	927.955.559.729	12
31	315.165	6
31	99.329.292.399	11
30	300.000	6
30	90.000.300.009	11
29	128.348	6
29	16.473.337.461	11
28	125.206	6
28	15.676.667.651	11
27	114.141	6
27	13.028.282.031	11
26	Prime! 106.801	6
26	Prime! 11.406.560.411	11
25	72.062	5
25	5.193.003.915	10
24	30.605	5
24	936.696.639	9
23	30.000	5
23	900.030.009	9
22	9.854	4
22	97.111.179	8
21	Prime! 3.881	4
21	15.066.051	8
20	3.144	4
20	9.887.889	7
19	3.000	4
19	9.003.009	7
18	2.367	4
18	5.605.065	7
17	1.413	4
17	1.997.991	7
16	1.141	4
16	Prime! 1.303.031	7
15	969	3
15	939.939	6
14	438	3
14	192.291	6
13	Prime! 331	3
13	109.901	6
12	305	3
12	93.339	5
11	304	3
11	92.729	5
10	300	3
10	90.309	5
9	138	3
9	19.191	5
8	Prime! 31	2
8	1.001	4
7	30	2
7	939	3
6	22	2
6	515	3
5	Prime! 13	2
5	Prime! 191	3
4	Prime! 11	2
4	141	3
3	9	1
3	99	2
2	1	1
2	Prime! 11	2
1	0	1
1	9	1

Further Topics Revealed

Neil Sloane's "Integer Sequences" Encyclopedia can be consulted online :

Neil Sloane's Integer Sequences

If you are interested in the primes of these numbers rather than the palindromes,
well look no further :
%N n^2 + n + 1 is prime. under A002384

%N Primes of form n^2 + n + 1. under A002383

%N n^2 + n + 3 is prime. under A027752

%N Primes of form n^2 + n + 3. under A027753

%N n^2 + n + 5 is prime. under A027754

%N Primes of form n^2 + n + 5. under A027755

%N n^2 + n + 7 is prime. under A027756

%N Primes of form n^2 + n + 7. or [n^2 + 3n+9] under A005471

%N n^2 + n + 9 is prime. under A027757

%N Primes of form n^2 + n + 9. under A027758

Two more formula's are included in the table. They are well known to prime-lovers.
n² + n + 17 generates 16 primes for all n values 0 to 15 !

%N n^2 + n + 17 is prime. under A028823

%N n^2 + n + 17 is composite. under A007636

%N Primes of form n^2 + n + 17. under A007635

n² + n + 41 generates 40 primes for all n values 0 to 39 !

%N n^2 + n + 41 is prime. under A002837

%N n^2 + n + 41 is composite. under A007634

%N Primes of form n^2 + n + 41. under A005846

Click here to view some of the author's [P. De Geest] entries to the table.
Click here to view some entries to the table about palindromes.

Contributions

Copy & pasted from the OEIS Encyclopedia many more results from Giovanni Resta as indicated in the headings.

[ November 3, 2022 ]
Contribution from Robert Xiao (email)

“ I'm still working on some upgrades to the program, but in the meantime, I thought I'd share
the length-40 and length-41 entries for Case X = 2 [n^2 + n + 2] found by my program:

[ See entries [116] up to [121] in the table.]

Length-40 took 229 seconds and length-41 took 689 seconds on my machine to generate.

Best,
Robert.”

[ November 11, 2022 ]
Robert Xiao (email) added

for Case X = 2 [n^2 + n + 2] entries [122] up to [128].

for Case X = 3 [n^2 + n + 3] entries [126] up to [188], except entry [167] which was already known.

for Case X = 4 [n^2 + n + 4] entries [58] up to [70].

for Case X = 5 [n^2 + n + 5] entries [80] up to [87].

for Case X = 6 [n^2 + n + 6] entries [55] up to [63].

for Case X = 7 [n^2 + n + 7] entries [72] up to [80].

for Case X = 8 [n^2 + n + 8] entries [33] up to [41].

for Case X = 9 [n^2 + n + 9] entries [118] up to [139].

[ December 6, 2022 ]
Robert Xiao (email) added

for Case X = 2 [n^2 + n + 2] entries [129] up to [152].

for Case X = 3 [n^2 + n + 3] entries [189] up to [316], except entry [286] which was already known.

for Case X = 4 [n^2 + n + 4] entries [71] up to [77].

for Case X = 5 [n^2 + n + 5] entries [88] up to [94].

for Case X = 6 [n^2 + n + 6] entries [64] up to [75].

for Case X = 7 [n^2 + n + 7] entries [81] up to [96].

for Case X = 8 [n^2 + n + 8] entries [42] up to [45].

for Case X = 9 [n^2 + n + 9] entries [140] up to [164].

[ June 22, 2023 ]
Patrick De Geest (email) added

for Case X = 2 [n^2 + n + 2] entries [153] up to [155].

for Case X = 3 [n^2 + n + 3] entries [317] up to [352].

for Case X = 4 [n^2 + n + 4] entries [78] up to [81].

for Case X = 6 [n^2 + n + 6] entries [76] up to [78].

for Case X = 7 [n^2 + n + 7] entries [97] up to [99].

for Case X = 8 [n^2 + n + 8] entry [46].

for Case X = 9 [n^2 + n + 9] entry [165].

[ July 18, 2023 ]
Patrick De Geest (email) added

for Case X = 2 [n^2 + n + 2] entries [156] up to [161].

for Case X = 3 [n^2 + n + 3] entries [353] up to [392].

for Case X = 4 [n^2 + n + 4] entry [82].

for Case X = 5 [n^2 + n + 5] entries [95] up to [97].

for Case X = 6 [n^2 + n + 6] entry [79].

for Case X = 7 [n^2 + n + 7] entries [100] up to [103].

for Case X = 8 [n^2 + n + 8] entry [47].

for Case X = 9 [n^2 + n + 9] entry [166] up to [170].

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