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



Introduction

Palindromic numbers are numbers which read the same from
 p_right left to right (forwards) as from the right to left (backwards) p_left
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

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 }.

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

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

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

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

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

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


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 BasenumberLength
Palindromic Quasi_Over_Squares of form n^2+(n+X)Length
up down
Case X = 0
See in-depth webpage about Palindromic Pronic Numbers
up down
Case X = 1
See in-depth webpage about Palindromic Quasi-Over-Squares
up down
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. From Index Nr 51 up to 65.
More terms from Patrick De Geest, from Sep 1, 2020. From Index Nr 66 up to 115.
11522.349.935.885.854.845.65620
499.519.634.101.822.224.454.422.228.101.436.915.99439
11421.648.788.975.466.017.94620
468.670.064.104.258.998.989.899.852.401.460.076.86439
11320.000.000.000.000.000.00120
400.000.000.000.000.000.060.000.000.000.000.000.00439
11215.682.422.422.343.540.31520
245.938.373.032.823.434.777.434.328.230.373.839.54239
11115.647.015.327.334.577.78420
244.829.088.653.843.204.373.402.348.356.880.928.44239
11014.681.808.231.390.847.41020
215.555.492.943.336.042.818.240.633.349.294.555.51239
10914.468.011.600.019.886.09920
209.323.359.658.309.984.636.489.903.856.953.323.90239
108Prime!    2.837.459.270.361.355.69719
8.051.175.110.959.597.047.407.959.590.115.711.50837
1072.058.677.547.772.551.63319
4.238.153.245.702.806.613.166.082.075.423.518.32437
1062.000.000.000.000.000.00119
4.000.000.000.000.000.006.000.000.000.000.000.00437
1051.604.777.671.384.426.74919
2.575.311.374.574.023.168.613.204.754.731.135.75237
1041.472.063.339.927.111.61419
2.166.970.476.757.362.959.592.637.576.740.796.61237
103703.359.338.401.854.46818
494.714.358.917.094.430.034.490.719.853.417.49436
102664.384.175.944.617.41818
441.406.333.245.608.354.453.806.542.333.604.14436
101468.033.494.872.988.31418
219.055.352.323.023.578.875.320.323.253.550.91236
100200.000.000.000.000.00118
40.000.000.000.000.000.600.000.000.000.000.00435
9920.548.848.021.323.33317
422.255.155.003.443.878.344.300.551.552.22433
9820.000.000.000.000.00117
400.000.000.000.000.060.000.000.000.000.00433
976.850.109.083.855.64616
46.923.994.460.721.644.612.706.449.932.96432
964.514.881.483.507.32416
20.384.154.810.117.299.271.101.845.148.30232
952.916.449.084.541.63216
8.505.675.262.723.726.273.272.625.765.05831
942.829.855.733.529.60216
8.008.083.472.590.364.630.952.743.808.00831
932.188.234.330.424.21616
4.788.369.484.847.119.117.484.849.638.87431
922.067.032.967.032.95816
4.272.625.286.801.075.701.086.825.262.72431
912.000.000.000.000.00116
4.000.000.000.000.006.000.000.000.000.00431
901.572.610.479.725.85916
2.473.103.720.943.597.953.490.273.013.74231
891.542.828.488.662.80516
2.380.319.745.429.556.559.245.479.130.83231
881.488.667.854.682.27916
2.216.131.981.564.340.434.651.891.316.12231
87925.624.837.663.11215
856.781.340.098.863.368.890.043.187.65830
86222.473.255.490.46815
49.494.349.408.527.272.580.494.349.49429
85210.516.022.946.98115
44.316.995.917.414.041.471.959.961.34429
84200.000.000.000.00115
40.000.000.000.000.600.000.000.000.00429
8320.000.000.000.00114
400.000.000.000.060.000.000.000.00427
8214.754.699.832.48514
217.701.167.146.747.641.761.107.71227
815.270.176.390.87013
27.774.759.190.888.809.195.747.77226
804.904.746.291.44013
24.056.536.183.399.338.163.565.04226
792.925.116.099.26713
8.556.304.194.193.914.914.036.55825
782.838.046.790.77713
8.054.509.586.642.466.859.054.50825
772.084.206.947.11113
4.343.918.598.387.838.958.193.43425
762.071.648.052.43313
4.291.725.653.151.513.565.271.92425
752.067.032.967.04113
4.272.625.286.836.386.825.262.72425
742.015.098.740.20113
4.060.622.932.761.672.392.260.60425
732.000.000.000.00113
4.000.000.000.006.000.000.000.00425
721.644.864.716.95413
2.705.579.937.081.807.399.755.07225
711.549.917.788.44013
2.402.245.150.924.290.515.422.04225
701.511.192.351.79513
2.283.702.324.125.214.232.073.82225
69Prime!    899.201.757.55712
808.563.800.794.497.008.365.80824
68Prime!    684.374.223.05312
468.368.077.180.081.770.863.86424
67675.835.699.32312
456.753.892.480.084.298.357.65424
66654.264.529.13312
428.062.074.082.280.470.260.82424
65544.298.466.46512
296.260.820.596.695.028.062.69224
64200.000.000.00112
40.000.000.000.600.000.000.00423
63146.078.456.08512
21.338.915.332.323.351.983.31223
6289.921.234.44211
8.085.828.403.663.048.285.80822
6148.973.960.09411
2.398.448.767.337.678.448.93222
6048.762.480.70511
2.377.779.524.554.259.777.73222
5947.382.584.97911
2.245.109.359.339.539.015.42222
5820.000.000.00111
400.000.000.060.000.000.00421
576.383.911.90110
40.754.331.166.113.345.70420
562.916.938.79210
8.508.531.919.191.358.05819
552.137.594.67610
4.569.311.001.001.139.65419
542.092.486.16310
4.378.498.344.438.948.73419
53Prime!    2.089.713.86310
4.366.904.031.304.096.63419
522.069.010.86610
4.280.805.965.695.080.82419
512.067.032.95810
4.272.625.251.525.262.72419
502.000.000.00110
4.000.000.006.000.000.00419
491.553.608.45910
2.413.699.245.429.963.14219
481.434.631.49910
2.058.167.539.357.618.50219
47528.342.9299
279.146.251.152.641.97218
46482.441.6699
232.749.964.469.947.23218
45223.314.9569
49.869.569.796.596.89417
44213.934.6239
45.768.023.132.086.75417
43200.000.0019
40.000.000.600.000.00417
42161.280.5399
26.011.412.421.411.06217
4192.610.8528
8.576.770.000.776.75816
4048.829.9308
2.384.362.112.634.83216
3929.287.0528
857.731.444.137.75815
3822.012.0388
484.529.838.925.48415
3721.855.1088
477.645.767.546.77415
3621.147.9068
447.233.949.332.74415
3520.000.0018
400.000.060.000.00415
3417.101.8098
292.471.888.174.29215
3314.842.9958
220.314.515.413.02215
322.000.0017
4.000.006.000.00413
311.651.7547
2.728.292.928.27213
301.620.6607
2.626.540.456.26213
29501.4746
251.476.674.15212
28Prime!    219.0836
47.997.579.97411
27200.0016
40.000.600.00411
2689.7775
8.059.999.50810
2528.3775
805.282.5089
2420.9935
440.727.0449
2320.0015
400.060.0049
2216.7805
281.585.1829
212.1834
4.767.6747
202.1064
4.437.3447
192.0014
4.006.0047
181.6544
2.737.3727
171.5304
2.342.4327
161.4244
2.029.2027
158973
805.5086
14Prime!    4793
229.9226
132923
85.5585
122033
41.4145
112013
40.6045
10922
8.5584
9502
2.5524
8212
4643
7152
2423
6142
2123
561
442
441
222
3Prime!    21
81
211
41
101
Prime!    21
up down
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. From Index Nr 38 up to 50.
More terms from Patrick De Geest, from Sep 1, 2020. From Index Nr 51 up to 124.
1256.295.866.490.138.952.53419
39.637.934.861.654.573.311.337.545.616.843.973.69338
1243.009.909.909.909.909.90219
9.059.557.665.773.881.945.491.883.775.667.559.50937
1233.009.900.990.900.990.09719
9.059.503.975.026.762.073.702.676.205.793.059.50937
1223.009.900.909.909.009.90219
9.059.503.487.471.085.745.475.801.747.843.059.50937
1213.000.999.009.900.999.00219
9.005.995.057.426.776.309.036.776.247.505.995.00937
1203.000.990.990.099.099.00219
9.005.946.922.655.970.527.250.795.562.296.495.00937
1193.000.990.099.009.900.99719
9.005.941.574.355.455.391.935.545.534.751.495.00937
1183.000.990.090.909.900.99719
9.005.941.525.739.415.853.585.149.375.251.495.00937
1173.000.990.009.900.099.00219
9.005.941.039.520.196.309.036.910.259.301.495.00937
1163.000.900.990.099.009.00219
9.005.406.752.377.212.527.252.127.732.576.045.00937
1153.000.900.090.090.009.00219
9.005.401.350.702.224.147.414.222.070.531.045.00937
1143.000.099.009.900.990.00219
9.000.594.069.208.900.509.050.098.029.604.950.00937
1133.000.090.009.900.090.00219
9.000.540.067.502.322.129.212.232.057.600.450.00937
1121.987.476.933.990.142.63419
3.950.064.563.142.857.782.877.582.413.654.600.59337
1111.770.410.114.442.237.08519
Prime!    3.134.351.973.319.375.014.105.739.133.791.534.31337
110300.990.990.909.909.90218
90.595.576.608.929.465.556.492.980.667.559.50935
109300.900.909.090.900.90218
90.541.357.091.730.609.390.603.719.075.314.50935
108300.099.900.900.999.00218
90.059.950.520.789.421.912.498.702.505.995.00935
107300.099.009.990.099.00218
90.059.415.797.037.540.904.573.079.751.495.00935
106300.099.001.800.099.00218
90.059.410.881.415.824.342.851.418.801.495.00935
105300.099.000.900.099.00218
90.059.410.341.237.621.912.673.214.301.495.00935
104300.090.099.099.009.00218
90.054.067.577.253.043.734.035.277.576.045.00935
103300.090.090.009.009.00218
90.054.062.121.615.124.742.151.612.126.045.00935
102300.009.998.199.990.00218
90.005.999.019.958.004.540.085.991.099.950.00935
101300.009.000.900.090.00218
90.005.400.621.070.203.930.207.012.600.450.00935
10030.099.099.090.090.09717
905.955.766.035.062.535.260.530.667.559.50933
9930.099.090.099.090.09717
905.955.224.793.143.535.341.397.422.559.50933
9830.099.009.090.990.09717
905.950.348.259.504.535.405.952.843.059.50933
9730.099.009.009.009.90217
905.950.343.324.459.272.954.423.343.059.50933
96Prime!    30.090.090.909.099.09717
905.413.570.917.848.151.848.719.075.314.50933
9530.009.990.990.999.00217
900.599.559.279.841.292.148.972.955.995.00933
9430.009.909.900.900.99717
900.594.692.260.195.717.591.062.296.495.00933
9330.009.900.990.099.00217
900.594.157.435.545.090.545.534.751.495.00933
92Prime!    30.009.009.900.990.99717
900.540.675.237.775.717.577.732.576.045.00933
9122.797.812.361.579.67117
519.740.248.473.794.878.497.374.842.047.91533
9022.683.451.840.157.82817
514.538.987.384.759.575.957.483.789.835.41533
8919.007.389.738.417.93517
361.280.864.668.115.434.511.866.468.082.16333
8817.587.931.732.323.90017
309.335.342.620.885.999.588.026.243.533.90333
873.009.909.909.909.90216
9.059.557.665.773.837.383.775.667.559.50931
863.009.900.909.009.90216
9.059.503.482.058.637.368.502.843.059.50931
853.009.090.090.090.90216
9.054.623.170.283.275.723.820.713.264.50931
843.009.009.090.900.90216
9.054.135.709.124.275.724.219.075.314.50931
833.000.990.999.099.00216
9.005.946.976.673.229.223.766.796.495.00931
823.000.990.090.099.00216
9.005.941.520.872.419.142.780.251.495.00931
813.000.900.090.009.00216
9.005.401.350.216.039.306.120.531.045.00931
802.434.467.459.876.86816
5.926.631.813.199.332.339.913.181.366.29531
792.328.650.332.630.59316
5.422.612.371.660.573.750.661.732.162.24531
781.746.916.031.844.12416
3.051.715.622.314.022.204.132.265.171.50331
77300.990.990.090.09715
90.595.576.115.417.171.451.167.559.50929
76300.990.099.009.90215
90.595.039.701.990.909.910.793.059.50929
75300.990.090.990.09715
90.595.034.874.227.172.247.843.059.50929
74300.900.909.099.09715
Prime!    90.541.357.096.663.336.669.075.314.50929
73300.090.099.009.00215
90.054.067.523.232.923.232.576.045.00929
72229.001.028.816.94115
52.441.471.199.217.671.299.117.414.42529
71198.267.378.873.16515
39.309.953.525.235.353.252.535.990.39329
70196.911.378.423.38015
38.774.090.952.595.759.525.909.047.78329
69185.315.401.886.74015
34.341.798.176.444.144.467.189.714.34329
68175.962.987.683.09915
30.962.973.034.362.626.343.037.926.90329
6730.099.009.009.90214
905.950.343.378.191.873.343.059.50927
6630.090.990.990.90214
905.467.738.814.575.418.837.764.50927
6530.090.090.900.90214
905.413.570.424.575.424.075.314.50927
6430.009.981.999.00214
900.599.019.580.454.085.910.995.00927
6330.009.009.009.00214
900.540.621.702.393.207.126.045.00927
6219.017.332.697.43914
361.658.942.925.101.529.249.856.16327
6118.349.377.330.60514
336.699.648.420.939.024.846.996.63327
6017.601.866.803.27514
309.825.714.960.252.069.417.528.90327
597.095.660.661.22613
50.348.400.219.277.291.200.484.30526
583.086.915.322.64713
9.529.046.209.195.919.026.409.25925
573.085.682.084.87213
9.521.433.928.903.098.293.341.25925
563.009.909.909.90213
9.059.557.665.729.275.667.559.50925
553.009.909.090.09713
9.059.552.730.651.560.372.559.50925
543.009.090.090.90213
9.054.623.175.167.615.713.264.50925
533.009.009.099.09713
9.054.135.758.451.548.575.314.50925
521.953.167.924.21913
3.814.864.940.199.910.494.684.18325
511.897.132.914.32513
3.599.113.294.617.164.923.119.95325
501.755.185.230.17513
3.080.675.192.226.222.915.760.80325
49300.990.909.90212
90.595.527.843.934.872.559.50923
48300.900.900.90212
90.541.352.163.936.125.314.50923
47181.723.112.00512
33.023.289.436.963.498.232.03323
4671.171.663.32611
5.065.405.660.660.665.045.60522
4557.747.550.56911
3.334.779.596.776.959.774.33322
4430.090.990.90211
905.467.733.494.337.764.50921
4322.486.248.62611
505.631.377.292.773.136.50521
4219.707.956.14411
388.403.535.393.535.304.88321
413.009.819.90210
9.059.015.845.485.109.50919
403.009.090.90210
9.054.628.059.508.264.50919
392.411.508.13810
5.815.371.502.051.735.18519
382.381.776.12110
5.672.857.492.947.582.76519
372.315.681.86310
5.362.382.492.942.832.63519
36727.913.4339
529.857.966.669.758.92518
35726.714.7419
528.114.315.513.411.82518
34589.167.8599
347.118.766.667.811.74318
33549.199.5249
301.620.117.711.026.10318
32Prime!    309.230.2879
95.623.370.707.332.65917
31230.098.5669
52.945.350.305.354.92517
30177.865.3859
31.636.095.359.063.61317
2976.675.1868
5.879.084.224.809.78516
2862.127.1808
3.859.786.556.879.58316
2730.909.0928
955.371.999.173.55915
2618.886.0258
356.681.959.186.65315
2517.605.7248
309.961.535.169.90315
245.492.8997
30.171.944.917.10314
233.093.8527
9.571.923.291.75913
22598.3506
358.023.320.85312
21237.7216
56.511.511.56511
20Prime!    230.6636
53.205.650.23511
1975.1465
5.646.996.46510
1873.1885
5.356.556.53510
1730.9475
957.747.7599
1623.1115
534.141.4359
156.1544
37.877.8738
142.4314
5.912.1957
137533
567.7656
122433
59.2955
111843
34.0435
10Prime!    1793
32.2235
91753
Prime!    30.8035
8Prime!    712
5.1154
7602
3.6634
6Prime!    232
5553
5Prime!    192
Prime!    3833
4Prime!    51
332
3Prime!    21
91
211
Prime!    51
101
Prime!    31
up down
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. From Index Nr 33 up to 36.
More terms from Patrick De Geest, from Sep 1, 2020. From Index Nr 37 up to 57.
572.456.920.322.636.915.22619
6.036.457.471.786.283.611.163.826.871.747.546.30637
562.019.265.573.385.942.29919
4.077.433.455.861.658.326.238.561.685.543.347.70437
552.000.000.000.000.000.00019
4.000.000.000.000.000.002.000.000.000.000.000.00437
54251.777.501.269.233.96318
63.391.910.145.379.110.101.197.354.101.919.33635
53200.000.000.000.000.00018
40.000.000.000.000.000.200.000.000.000.000.00435
5221.502.431.241.622.33917
462.354.549.300.696.424.696.003.945.453.26433
5120.000.000.000.000.00017
400.000.000.000.000.020.000.000.000.000.00433
502.464.706.598.254.90116
6.074.778.615.481.248.421.845.168.774.70631
492.209.415.043.638.51916
4.881.514.835.056.201.026.505.384.151.88431
482.103.611.085.905.64016
4.425.179.600.745.108.015.470.069.715.24431
472.000.000.000.000.00016
4.000.000.000.000.002.000.000.000.000.00431
46260.565.021.991.21615
67.894.130.685.283.138.258.603.149.87629
45220.867.190.255.61915
48.782.315.731.412.021.413.751.328.78429
44210.855.962.500.84015
44.460.236.922.155.855.122.963.206.44429
43200.000.000.000.00015
40.000.000.000.000.200.000.000.000.00429
4225.142.773.284.28814
632.159.048.425.131.524.840.951.23627
4125.075.537.810.13314
628.782.596.467.434.764.695.287.82627
4024.884.321.704.67114
619.229.466.701.585.107.664.922.91627
3920.217.027.652.82414
408.728.207.115.070.511.702.827.80427
3820.139.827.049.12414
405.612.633.568.646.865.336.216.50427
3720.000.000.000.00014
400.000.000.000.020.000.000.000.00427
362.537.387.874.01813
6.438.337.223.216.123.227.338.34625
352.451.351.151.12613
6.009.122.466.129.216.642.219.00625
342.007.806.131.30013
4.031.285.460.887.880.645.821.30425
332.000.000.000.00013
4.000.000.000.002.000.000.000.00425
32200.000.000.00012
40.000.000.000.200.000.000.00423
3124.784.431.17111
614.268.028.494.820.862.41621
3021.572.321.96011
465.365.074.767.470.563.56421
2920.349.812.81411
414.114.881.585.188.411.41421
2820.102.030.40011
404.091.626.222.626.190.40421
2720.000.000.00011
400.000.000.020.000.000.00421
262.094.600.19410
4.387.349.974.799.437.83419
252.000.000.00010
4.000.000.002.000.000.00419
24205.705.7049
42.314.836.863.841.32417
23200.000.0009
40.000.000.200.000.00417
2225.882.3538
669.896.222.698.96615
2120.000.0008
400.000.020.000.00415
202.620.4867
6.866.949.496.68613
192.490.2667
6.201.427.241.02613
182.155.1397
4.644.626.264.46413
172.000.0007
4.000.002.000.00413
16218.3546
47.678.687.67411
15205.7046
42.314.341.32411
14202.8856
41.162.526.11411
13200.0006
40.000.200.00411
1220.6045
424.545.4249
1120.0005
400.020.0049
102.6134
6.830.3867
9Prime!    2.5514
6.510.1567
82.2344
4.992.9947
72.0004
4.002.0047
62613
68.3865
52193
48.1845
42003
40.2045
3202
4243
211
61
101
41
up down
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. From Index Nr 30 up to 46.
More terms from Patrick De Geest, from Sep 1, 2020. From Index Nr 47 up to 79.
793.438.846.839.357.135.35719
11.825.667.584.556.559.511.595.565.548.576.652.81138
782.821.048.328.990.795.23119
7.958.313.674.501.758.047.408.571.054.763.138.59737
772.808.651.171.354.901.88619
7.888.521.402.353.262.439.342.623.532.041.258.88737
762.662.636.067.713.063.39819
7.089.630.829.086.485.135.315.846.809.280.369.80737
75Prime!    1.266.537.051.930.343.60719
1.604.116.103.912.405.899.985.042.193.016.114.06137
741.092.269.214.303.220.06219
1.193.052.036.514.573.674.763.754.156.302.503.91137
731.065.112.309.613.110.54219
1.134.464.232.089.374.652.564.739.802.324.644.31137
72854.071.216.890.041.43318
729.437.643.520.036.195.591.630.025.346.734.92736
71710.487.567.770.103.22418
504.792.583.955.877.022.220.778.559.385.297.40536
70272.740.912.616.759.10618
74.387.605.415.022.626.762.622.051.450.678.34735
69128.516.445.113.554.26718
16.516.476.664.625.206.560.252.646.667.461.56135
68127.555.335.548.680.95218
16.270.363.626.936.590.709.563.962.636.307.26135
67127.325.246.849.329.75218
16.211.718.485.242.756.065.724.258.481.711.26135
6673.856.398.697.590.94017
5.454.767.628.577.512.772.157.758.267.674.54534
6528.182.867.034.430.53117
794.273.994.280.391.181.193.082.499.372.49733
6424.124.980.160.964.11917
582.014.667.766.912.353.219.667.766.410.28533
6310.891.052.175.305.91717
118.615.017.485.235.757.532.584.710.516.81133
6210.742.267.540.559.29717
115.396.311.912.953.898.359.219.113.693.51133
617.649.794.162.480.81916
58.519.350.728.325.622.652.382.705.391.58532
607.200.217.655.047.41416
51.843.134.280.056.488.465.008.243.134.81532
59Prime!    2.709.031.479.580.96316
7.338.851.557.360.624.260.637.551.588.33731
582.689.612.932.909.63316
7.234.017.728.874.760.674.788.277.104.32731
572.391.927.132.618.75416
5.721.315.407.757.776.777.577.045.131.27531
561.274.252.737.050.15216
1.623.720.037.879.805.089.787.300.273.26131
55709.962.501.910.22415
504.046.754.118.625.526.811.457.640.40530
54266.915.367.273.77115
71.243.813.286.892.329.868.231.834.21729
53264.586.807.048.12615
70.006.178.463.922.522.936.487.160.00729
52128.523.687.718.10715
16.518.338.304.661.616.640.383.381.56129
51127.307.298.113.55215
16.207.148.152.972.927.925.184.170.26129
50107.441.307.275.09715
11.543.634.508.981.918.980.543.634.51129
49106.650.062.701.65715
11.374.235.874.267.476.247.853.247.31129
48104.926.659.615.12215
Prime!    11.009.603.897.987.778.979.830.690.01129
4710.685.559.255.23714
114.181.176.597.191.795.671.181.41127
462.724.617.501.71813
7.423.540.530.670.760.350.453.24725
452.413.553.760.25513
5.825.241.753.643.463.571.425.28525
441.274.687.352.35213
1.624.827.846.247.426.487.284.26125
431.092.675.882.73713
1.193.940.584.716.174.850.493.91125
42712.311.093.70012
507.387.094.208.802.490.783.70524
41128.760.203.49212
16.579.190.003.430.009.197.56123
40127.651.865.35212
16.294.998.727.972.789.949.26123
3987.304.087.37811
7.622.003.672.992.763.002.26722
3884.526.784.82811
7.144.777.353.443.537.774.41722
3727.413.239.44811
751.485.697.060.796.584.15721
3624.070.821.94511
579.404.469.131.964.404.97521
3523.203.983.19411
538.424.836.090.638.424.83521
344.029.203.52710
16.234.481.066.018.443.26120
332.815.069.13110
7.924.614.215.124.164.29719
322.781.875.71610
Prime!    7.738.832.502.052.388.37719
312.765.569.14610
7.648.372.704.072.738.46719
302.426.472.51910
5.887.768.887.888.677.88519
292.237.334.99910
5.005.667.899.987.665.00519
28Prime!    106.617.6179
11.367.316.361.376.31117
2787.579.7538
7.670.213.223.120.76716
2685.125.9338
7.246.424.554.246.42716
257.569.2457
57.293.477.439.27514
244.063.8927
16.515.222.251.56114
232.775.3837
7.702.753.572.07713
222.724.7187
Prime!    7.424.090.904.24713
212.358.1507
5.560.873.780.65513
20107.4226
11.539.593.51111
19105.3226
11.092.829.01111
1828.1685
793.464.3979
1727.5485
758.919.8579
1622.4245
502.858.2059
1512.7525
162.626.2619
144.0674
16.544.5618
134.0124
16.100.1618
123.4624
11.988.9118
112.7514
7.570.7577
102303
53.1355
92243
50.4055
8Prime!    1273
16.2615
7742
5.5554
6262
7073
5122
1613
481
772
3Prime!    21
Prime!    112
211
Prime!    71
101
Prime!    51
up down
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. From Index Nr 32 up to 34.
More terms from Patrick De Geest, from Sep 1, 2020. From Index Nr 35 up to 54.
542.985.831.125.619.083.43119
8.915.187.510.715.722.782.872.275.170.157.815.19837
532.916.855.303.079.661.85119
8.508.044.859.103.945.996.995.493.019.584.408.05837
522.551.552.617.878.235.47419
6.510.420.761.801.276.736.376.721.081.670.240.15637
511.463.508.671.957.677.63719
2.141.857.632.895.325.294.925.235.982.367.581.41237
50254.045.687.862.089.94018
64.539.211.521.322.432.123.422.312.511.293.54635
49162.090.760.203.886.32718
26.273.414.543.473.779.597.737.434.541.437.26235
48147.870.657.622.296.95718
21.865.731.385.650.569.296.505.658.313.756.81235
4729.498.083.994.743.00817
870.136.959.360.913.646.319.063.959.631.07833
4614.500.619.401.279.59717
210.267.963.020.766.272.667.020.369.762.01233
45287.460.767.600.65815
82.633.692.909.559.795.590.929.633.62829
44255.814.556.383.82515
65.441.087.257.853.435.875.278.014.45629
43162.126.124.865.15215
26.284.880.363.791.019.736.308.848.26229
4226.199.714.854.34414
686.425.058.448.959.844.850.524.68627
412.610.993.061.21913
6.817.284.765.736.375.674.827.18625
402.565.389.200.64913
6.581.221.750.809.080.571.221.85625
392.497.478.799.07913
6.237.400.351.851.581.530.047.32625
381.630.700.084.69213
2.659.182.766.216.126.672.819.56225
371.614.498.398.96713
2.606.605.080.268.620.805.066.06225
36293.212.995.77612
85.973.860.892.229.806.837.95823
35286.306.469.67112
81.971.394.575.757.549.317.91823
3429.959.390.36811
897.565.071.252.170.565.79821
3328.988.127.11811
840.311.513.838.315.113.04821
322.931.604.15110
8.594.302.901.092.034.95819
312.853.889.20310
8.144.683.585.853.864.41819
30288.888.8889
83.456.789.898.765.43817
29264.056.4349
69.725.800.600.852.79617
28148.278.1379
21.986.406.060.468.91217
2729.585.5088
875.302.313.203.57815
2629.190.7488
852.099.797.990.25815
2528.888.8888
834.567.878.765.43815
2416.353.5478
267.438.515.834.76215
2314.604.6578
213.296.020.692.31215
222.995.6317
8.973.808.083.79813
21Prime!    2.985.9437
8.915.858.585.19813
202.960.8167
8.766.434.346.67813
192.952.3167
8.716.172.716.17813
182.888.8887
8.345.676.765.43813
172.873.2337
8.255.470.745.52813
16Prime!    2.834.1017
8.032.131.312.30813
15292.2766
85.425.552.45811
14288.8886
83.456.565.43811
13264.3346
69.872.727.89611
12Prime!    146.7776
21.543.634.51211
1128.8885
834.545.4389
102.9464
8.681.8687
92.8884
8.343.4387
82.5504
6.505.0567
72.4854
6.177.7167
62883
83.2385
5282
8183
4252
6563
3242
6063
211
81
101
61
up down
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. From Index Nr 28 up to 45.
More terms from Patrick De Geest, from Sep 1, 2020. From Index Nr 46 up to 71.
713.121.000.000.000.001.20819
9.740.641.000.000.007.543.457.000.000.001.460.47937
703.021.993.199.130.681.09619
9.132.442.895.592.088.370.738.802.955.982.442.31937
693.000.000.000.000.000.00119
9.000.000.000.000.000.009.000.000.000.000.000.00937
682.722.509.353.145.589.45919
7.412.057.177.965.215.939.395.125.697.717.502.14737
671.915.035.496.742.374.88719
3.667.360.953.783.314.538.354.133.873.590.637.66337
66312.100.000.000.001.20818
97.406.410.000.000.754.345.700.000.001.460.47935
65300.000.000.000.000.00118
90.000.000.000.000.000.900.000.000.000.000.00935
64277.182.107.823.074.73918
76.829.920.897.242.630.703.624.279.802.992.86735
63191.130.616.729.367.09218
36.530.912.651.348.219.891.284.315.621.903.56335
6231.210.000.000.001.20817
974.064.100.000.075.434.570.000.001.460.47933
6130.648.097.516.689.38817
939.305.881.392.502.262.205.293.188.503.93933
6030.000.000.000.000.00117
900.000.000.000.000.090.000.000.000.000.00933
5919.124.750.677.376.13217
365.756.088.471.798.838.897.174.880.657.56333
583.137.955.834.553.08616
9.846.766.819.605.757.575.069.186.676.48931
573.121.000.000.001.20816
9.740.641.000.007.543.457.000.001.460.47931
563.083.258.898.592.14816
9.506.485.435.747.668.667.475.345.846.05931
553.000.000.000.000.00116
9.000.000.000.000.009.000.000.000.000.00931
542.702.530.723.613.86916
7.303.672.312.076.905.096.702.132.763.03731
53312.100.000.001.20815
97.406.410.000.754.345.700.001.460.47929
52300.000.000.000.00115
90.000.000.000.000.900.000.000.000.00929
51268.792.508.783.80415
72.249.412.778.291.619.287.721.494.22729
50264.773.198.830.10015
70.104.846.818.723.932.781.864.840.10729
49177.377.074.711.83715
31.462.626.633.328.782.333.662.626.41329
4831.210.000.001.20814
974.064.100.075.434.570.001.460.47927
4730.000.000.000.00114
900.000.000.000.090.000.000.000.00927
4617.615.399.751.39714
310.302.308.401.535.104.803.203.01327
453.149.974.520.75613
9.922.339.481.415.141.849.332.29925
443.121.000.001.20813
9.740.641.007.543.457.001.460.47925
433.041.875.952.76613
9.253.009.312.019.102.139.003.52925
423.000.000.000.00113
9.000.000.000.009.000.000.000.00925
412.702.976.653.99413
7.306.082.792.039.302.972.806.03725
401.900.006.888.01213
3.610.026.174.494.944.716.200.16325
39312.100.001.20812
97.406.410.754.345.701.460.47923
38300.000.000.00112
90.000.000.000.900.000.000.00923
37281.757.625.70912
79.387.359.645.454.695.378.39723
36275.313.182.74912
75.797.348.595.659.584.379.75723
35266.584.070.21412
71.067.066.492.129.466.076.01723
3431.210.001.20811
974.064.175.434.571.460.47921
3331.006.644.07811
Prime!    961.411.977.010.779.114.16921
3230.805.056.48111
948.951.504.828.405.159.84921
31Prime!    30.000.000.00111
900.000.000.090.000.000.00921
3028.255.878.33411
798.394.660.454.066.493.89721
2926.928.832.87911
725.162.040.252.040.261.52721
283.121.001.20810
9.740.648.543.458.460.47919
273.000.000.00110
9.000.000.009.000.000.00919
262.817.818.39010
7.940.100.481.840.010.49719
252.673.533.18510
7.147.779.693.969.777.41719
24303.758.4589
92.269.201.110.296.22917
23300.000.0019
90.000.000.900.000.00917
2230.122.0988
907.340.818.043.70915
21Prime!    30.000.0018
900.000.090.000.00915
2027.515.1258
757.082.131.280.75715
193.000.0017
9.000.009.000.00913
181.762.1227
3.105.075.705.01313
17312.2086
97.474.147.47911
16300.0016
90.000.900.00911
15177.2376
31.413.131.41311
1430.0015
900.090.0099
13Prime!    27.2595
743.080.3479
12Prime!    3.0014
9.009.0097
112.7644
7.642.4677
10Prime!    1.7774
3.159.5137
9Prime!    3133
98.2895
83013
90.9095
72803
78.6875
62743
75.3575
51773
Prime!    31.5135
4Prime!    312
9993
3Prime!    172
Prime!    3133
211
91
101
Prime!    71
up down
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. From Index Nr 16 up to 19.
More terms from Patrick De Geest, from Sep 1, 2020. From Index Nr 20 up to 32.
322.919.019.406.760.380.37419
8.520.674.297.043.722.974.792.273.407.924.760.25837
312.896.827.497.610.422.90519
8.391.609.550.911.864.724.274.681.190.559.061.93837
30204.899.512.505.754.53718
41.983.810.225.095.860.106.859.052.201.838.91435
2929.293.314.111.168.35017
858.098.251.615.574.808.475.516.152.890.85833
2828.989.019.759.841.18417
840.363.266.636.462.646.264.636.662.363.04833
2721.622.406.372.184.97217
467.528.457.323.905.303.509.323.754.825.76433
2621.459.803.444.244.99217
460.523.163.865.629.242.926.568.361.325.06433
252.989.063.335.060.29016
8.934.499.621.001.746.471.001.269.944.39831
242.930.792.062.562.64916
8.589.542.113.980.229.220.893.112.459.85831
23Prime!    2.927.399.306.452.84916
8.569.666.699.420.624.260.249.966.669.65831
222.162.277.851.899.02716
4.675.445.508.813.072.703.188.055.445.76431
21288.191.799.404.99415
83.054.513.244.288.588.244.231.545.03829
20286.006.098.215.51415
81.799.488.216.462.526.461.288.499.71829
1921.614.586.653.85214
467.190.356.216.898.612.653.091.76427
1821.495.814.697.07214
462.070.049.490.878.094.940.070.26427
17295.431.039.62912
87.279.499.176.567.199.497.27823
16202.542.945.59712
41.023.644.811.311.844.632.01423
152.926.428.84910
8.563.985.811.185.893.65819
14287.010.9209
82.375.268.486.257.32817
132.997.3347
8.984.014.104.89813
122.990.3907
8.942.435.342.49813
112.837.8757
8.053.537.353.50813
102.834.6997
8.035.521.255.30813
9297.1196
88.279.997.28811
829.5705
874.414.4789
720.3775
415.242.5149
62.9354
8.617.1687
52.9254
8.558.5587
42853
81.5185
32023
41.0145
2Prime!    292
8783
101
81
up down
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 Nr 64 up to 71.
More terms from Patrick De Geest, from Sep 1, 2020. From Index Nr 72 up to 117.
1179.520.691.133.001.233.97519
90.643.559.650.008.320.288.202.380.005.695.534.60938
1163.897.012.554.826.686.29319
15.186.706.852.476.816.644.661.867.425.860.768.15138
1153.422.795.298.433.113.90119
11.715.527.654.975.829.255.292.857.945.672.551.71138
1143.069.325.912.785.429.98419
9.420.761.558.896.112.951.592.116.988.551.670.24937
1133.027.632.478.680.776.51019
9.166.558.425.962.702.631.362.072.695.248.556.61937
1123.000.000.000.000.000.00019
9.000.000.000.000.000.003.000.000.000.000.000.00937
1112.383.224.109.158.209.82719
5.679.757.154.472.942.831.382.492.744.517.579.76537
1101.407.464.140.369.542.23819
1.980.955.306.426.174.497.944.716.246.035.590.89137
1091.390.255.830.520.081.73819
1.932.811.274.295.082.238.322.805.924.721.182.39137
1081.158.845.561.992.536.06619
1.342.923.036.549.796.751.576.979.456.303.292.43137
1071.085.720.773.447.473.97319
1.178.789.597.895.381.106.011.835.987.959.878.71137
106968.166.647.234.714.83018
937.346.656.817.708.749.947.807.718.656.643.73936
105403.850.324.398.604.04818
163.095.084.516.857.724.427.758.615.480.590.36136
104300.000.000.000.000.00018
90.000.000.000.000.000.300.000.000.000.000.00935
103136.883.299.310.520.48318
18.737.037.630.133.537.473.533.103.673.073.78135
102100.101.032.507.332.34318
10.020.216.709.034.006.560.043.090.761.202.00135
10131.159.467.620.387.04517
970.912.422.385.948.727.849.583.224.219.07933
10030.000.000.000.000.00017
900.000.000.000.000.030.000.000.000.000.00933
9922.788.502.426.511.66217
519.315.842.843.127.929.721.348.248.513.91533
9813.718.360.536.465.21617
188.193.415.808.446.222.644.808.514.391.88133
9711.731.882.304.045.04117
137.637.062.395.965.191.569.593.260.736.73133
9611.578.846.113.932.06617
134.069.677.330.119.717.911.033.776.960.43133
953.262.179.310.062.14316
10.641.813.850.997.522.579.905.831.814.60132
943.000.000.000.000.00016
9.000.000.000.000.003.000.000.000.000.00931
931.411.031.348.053.41316
1.991.009.465.189.433.349.815.649.001.99131
921.361.700.097.732.88316
1.854.227.156.165.744.475.616.517.224.58131
911.325.889.400.817.84616
1.757.982.703.201.108.011.023.072.897.57131
901.006.850.261.673.26816
1.013.747.449.431.529.251.349.447.473.10131
89951.322.744.355.12415
905.014.963.927.365.563.729.369.410.50930
88370.656.884.454.04115
137.386.525.993.176.671.399.525.683.73130
87302.985.210.998.58515
91.800.038.083.857.375.838.083.000.81929
86300.207.281.032.10015
90.124.411.584.686.568.648.511.442.10929
85300.000.000.000.00015
90.000.000.000.000.300.000.000.000.00929
8441.989.656.355.54614
1.763.131.240.856.886.580.421.313.67128
8341.944.248.388.15314
1.759.319.972.847.117.482.799.139.57128
8230.000.000.000.00014
900.000.000.000.030.000.000.000.00927
8114.016.755.641.63814
196.469.438.717.404.717.834.964.69127
8012.977.693.492.54814
168.420.528.386.535.683.825.024.86127
7912.389.095.521.10614
153.489.687.831.101.138.786.984.35127
7811.270.747.729.27114
127.029.754.376.878.673.457.920.72127
77Prime!    3.809.272.592.56313
14.510.557.684.455.448.675.501.54126
763.000.000.000.00013
9.000.000.000.003.000.000.000.00925
751.379.803.137.28613
1.903.856.697.665.667.966.583.09125
741.179.335.179.43313
1.390.831.465.449.445.641.380.93125
731.161.363.821.93313
1.348.765.926.895.986.295.678.43125
72Prime!    720.082.209.31712
518.518.388.175.571.883.815.81524
71300.000.000.00012
90.000.000.000.300.000.000.00923
70226.596.191.58212
51.345.834.039.693.043.854.31523
69225.969.524.07712
51.062.225.811.811.852.226.01523
68107.716.960.20112
11.602.943.515.051.534.920.61123
6730.000.000.00011
900.000.000.030.000.000.00921
6611.950.115.33611
142.805.256.555.652.508.24121
6511.430.454.73311
130.655.295.414.592.556.03121
64Prime!    3.040.137.97910
9.242.438.934.398.342.42919
633.000.000.00010
9.000.000.003.000.000.00919
621.078.247.67310
1.162.618.045.408.162.61119
61989.943.0549
979.987.251.152.789.97918
60387.851.9939
150.429.168.861.924.05118
59349.101.6969
121.871.994.499.178.12118
58Prime!    346.313.5739
119.933.091.190.339.91118
57337.310.8989
113.778.642.246.877.31118
56302.382.6899
91.435.290.909.253.41917
55300.000.0009
90.000.000.300.000.00917
54128.536.6489
16.521.670.007.612.56117
53120.588.4369
14.541.571.017.514.54117
52109.666.0039
12.026.632.323.662.02117
5198.066.4398
9.617.026.556.207.16916
50Prime!    41.794.8538
1.746.809.779.086.47116
4935.409.4968
1.253.832.442.383.52116
4830.880.2748
953.591.353.195.35915
4730.592.6308
935.909.040.909.53915
4630.447.6958
927.062.161.260.72915
4530.000.0008
900.000.030.000.00915
4423.683.3928
560.903.080.309.06515
4313.220.9788
174.794.272.497.47115
4210.222.4568
104.498.616.894.40115
417.489.3927
56.091.000.019.06514
403.932.8067
15.466.966.966.45114
393.152.2907
9.936.935.396.39913
383.045.6797
9.276.163.616.72913
373.040.6047
9.245.275.725.42913
363.000.0007
9.000.003.000.00913
35Prime!    2.378.5077
5.657.297.927.56513
34989.1546
978.426.624.87912
33980.5606
961.498.894.16912
32963.3046
927.955.559.72912
31315.1656
99.329.292.39911
30300.0006
90.000.300.00911
29128.3486
16.473.337.46111
28125.2066
15.676.667.65111
27114.1416
13.028.282.03111
26Prime!    106.8016
Prime!    11.406.560.41111
2572.0625
5.193.003.91510
2430.6055
936.696.6399
2330.0005
900.030.0099
229.8544
97.111.1798
21Prime!    3.8814
15.066.0518
203.1444
9.887.8897
193.0004
9.003.0097
182.3674
5.605.0657
171.4134
1.997.9917
161.1414
Prime!    1.303.0317
159693
939.9396
144383
192.2916
13Prime!    3313
109.9016
123053
93.3395
113043
92.7295
103003
90.3095
91383
19.1915
8Prime!    312
1.0014
7302
9393
6222
5153
5Prime!    132
Prime!    1913
4Prime!    112
1413
391
992
211
Prime!    112
101
91




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.







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( © All rights reserved ) - Last modified : September 28, 2021.
Patrick De Geest - Belgium flag - Short Bio - Some Pictures
E-mail address : pdg@worldofnumbers.com