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EMBED
Palindromic Decremented Squares
of the form n^2–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
rood n^2+(n+1) rood n^2+(n+x)



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

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

base2 – X

     PLAIN TEXT SQUDECN 

Palindromic Decremented Squares

Decremented Squares of the form x2 – 0 can only start or end with a 0, 1, 4, 5, 6 or 9
Alas, my palindromes may not have leading 0's! So the zero option must not be investigated.
1 can only be followed by an even number : 10, 12, 14, 16 or 18
4 can only be followed by an even number : 40, 42, 44, 46 or 48
5 can only be followed by 2 : 52
6 can only be followed by an odd number : 61, 63, 65, 67 or 69
9 can only be followed by an even number : 90, 92, 94, 96 or 98

Decremented Squares of the form x2 – 1 can only start or end in one of the following digits : 0, 3, 4, 5, 8 or 9.
Alas, my palindromes may not have leading zero's! So the zero option must not be investigated.
3 can only be followed by an even number : 30, 32, 34, 36 or 38
4 can only be followed by 2 : 42
5 can only be followed by an odd number : 51, 53, 55, 57, 59
8 can only be followed by an even number : 80, 82, 84, 86 or 88
9 can only be followed by 9 : 99
Also Palindromic Quasipronics of the form x*(x + 2).
Proof by substitution whereby x equals  n – 1 
x * ( x + 2 ) =
      (n – 1) * ( (n – 1) + 2 ) =
      (n – 1) * (n + 1) =
      n2 + n –n – 1 =
n2 – 1 [ QED ]

Decremented Squares of the form x2 – 2 can only start or end with a 2, 3, 4, 7, 8 or 9.
Even length palindromes of this form are not possible as they are never divisible by 11.
2 can only be followed by an even number : 20, 22, 24, 26 or 28
3 can only be followed by 2 : 32
4 can only be followed by an odd number : 41, 43, 45, 47 or 49
7 can only be followed by an even number : 70, 72, 74, 76 or 78
8 can only be followed by 9 : 89
9 can only be followed by an odd number : 91, 93, 95, 97 or 99
bu17 There are no palindromic Decremented Squares of type x^2 – 2 of EVEN lengths.

Decremented Squares of the form x2 – 3 can only start or end with a 1, 2, 3, 6, 7 or 8.
1 can only be followed by an even number : 10, 12, 14, 16 or 18
2 can only be followed by 2 : 22
3 can only be followed by an odd number : 31, 33, 35, 37 or 39
6 can only be followed by an even number : 60, 62, 64, 66 or 68
7 can only be followed by 9 : 79
8 can only be followed by an odd number : 81, 83, 85, 87 or 89
bu17 There are no palindromic Decremented Squares of type x^2 – 3 of lengths 6, 8, 18, 24, 28, 48, 52.

Decremented Squares of the form x2 – 4 can only end with a 0, 1, 2, 5, 6 or 7.
And if it terminates in 1, it terminates in 21; if it terminates in 6, it terminates in 96 only.
Alas, my palindromes may not have leading zero's! So the zero option must not be investigated.
1 can only be followed by 2 : 12
2 can only be followed by an odd number : 21, 23, 25, 27 or 29
5 can only be followed by an even number : 50, 52, 54, 56 or 58
6 can only be followed by 9 : 69
7 can only be followed by an odd number : 71, 73, 75, 77 or 79
Also Palindromic Quasipronics of the form x*(x + 4).
Proof by substitution whereby x equals  n – 2 
x * ( x + 4 ) =
      (n – 2) * ( (n – 2) + 4 ) =
      (n – 2) * (n + 2) =
      n2 + 2n –2n – 4 =
n2 – 4 [ QED ]

Decremented Squares of the form x2 – 5 can only start or end with a 0, 1, 4, 5, 6 or 9.
Alas, my palindromes may not have leading 0's! So the zero option must not be investigated.
1 can only be followed by an odd number : 11, 13, 15, 17 or 19
4 can only be followed by an even number : 40, 42, 44, 46 or 48
5 can only be followed by 9 : 59
6 can only be followed by an odd number : 61, 63, 65, 67 or 69
9 can only be followed by an odd number : 91, 93, 95, 97 or 99
bu17 There are no palindromic Decremented Squares of type x^2 – 5 of lengths 14, 18, 32, 35, 44, 45, 49, 50.

Decremented Squares of the form x2 – 6 can only start or end with a 0, 3, 4, 5, 8 or 9.
Alas, my palindromes may not have leading 0's! So the zero option must not be investigated.
Even length palindromes of this form are not possible as they are never divisible by 11.
3 can only be followed by an even number : 30, 32, 34, 36 or 38 { This 36... produces ever expanding Mandelbrot-like infinite palindromes }
4 can only be followed by 9 : 49
5 can only be followed by an odd number : 51, 53, 55, 57 or 59
8 can only be followed by an odd number : 81, 83, 85, 87 or 89 { This 89... produces ever expanding Mandelbrot-like infinite palindromes }
9 can only be followed by 1 : 91
bu17 There are no palindromic Decremented Squares of type x^2 – 6 of EVEN length nor of length 3.

Decremented Squares of the form x2 – 7 can only start or end with a 2, 3, 4, 7, 8 or 9.
Even length palindromes of this form are not possible as they are never divisible by 11.
2 can only be followed by an even number : 20, 22, 24, 26 or 28
3 can only be followed by 9 : 39
4 can only be followed by an odd number : 41, 43, 45, 47 or 49
7 can only be followed by an odd number : 71, 73, 75, 77 or 79 { This 77... produces ever expanding Mandelbrot-like infinite palindromes }
8 can only be followed by 1 : 81
9 can only be followed by an even number : 90, 92, 94, 96 or 98
bu17 There are no palindromic Decremented Squares of type x^2 – 7 of EVEN length.

Decremented Squares of the form x2 – 8 can only start or end with a 1, 2, 3, 6, 7 or 8.
Even length palindromes of this form are not possible as they are never divisible by 11.
1 can only be followed by an even number : 10, 12, 14, 16 or 18
2 can only be followed by 9 : 29
3 can only be followed by an odd number : 31, 33, 35, 37 or 39
6 can only be followed by an odd number : 61, 63, 65, 67 or 69
7 can only be followed by 1 : 71
8 can only be followed by an even number : 80, 82, 84, 86 or 88
bu17 There are no palindromic Decremented Squares of type x^2 – 8 of EVEN length.

Decremented Squares of the form x2 – 9 can only start or end with a 0, 1, 2, 5, 6 or 7.
Alas, my palindromes may not have leading 0's! So the zero option must not be investigated.
1 can only be followed by 9 : 19
2 can only be followed by an odd number : 21, 23, 25, 27 or 29
5 can only be followed by an odd number : 51, 53, 55, 57 or 59
6 can only be followed by 1 : 61
7 can only be followed by an even number : 70, 72, 74, 76 or 78
Also Palindromic Decremented Squares of the form x*(x + 6).
Proof by substitution whereby x equals  n – 3 
x * ( x + 6 ) =
      (n – 3) * ( (n – 3) + 6 ) =
      (n – 3) * (n + 3) =
      n2 + 3n –3n – 9 =
n2 – 9 [ QED ]

Decremented SquaresChange of variablesCUDApalin parametersBase Correction
x^2 – 0n = m + 3
A B C →  1 6 9
base = CUDAbase + 3
x^2 – 1n = m + 3
A B C →  1 6 8
base = CUDAbase + 3
x^2 – 2n = m + 3
A B C →  1 6 7
base = CUDAbase + 3
x^2 – 3n = m + 3
A B C →  1 6 6
base = CUDAbase + 3
x^2 – 4n = m + 3
A B C →  1 6 5
base = CUDAbase + 3
x^2 – 5n = m + 3
A B C →  1 6 4
base = CUDAbase + 3
x^2 – 6n = m + 3
A B C →  1 6 3
base = CUDAbase + 3
x^2 – 7n = m + 3
A B C →  1 6 2
base = CUDAbase + 3
x^2 – 8n = m + 3
A B C →  1 6 1
base = CUDAbase + 3
x^2 – 9n = m + 3
A B C →  1 6 0
base = CUDAbase + 3

An infinite palindromic pattern hides in the list for case n^2 – 2

302 – 2 = 898
3002 – 2 = 89998
30002 – 2 = 8999998
300002 – 2 = 899999998
3000002 – 2 = 89999999998
30000002 – 2 = 8999999999998
300000002 – 2 = 899999999999998

Two infinite palindromic pattern hide in the list for case n^2 – 3

292 – 3 = 838
2992 – 3 = 89398
29992 – 3 = 8993998
299992 – 3 = 899939998
2999992 – 3 = 89999399998
29999992 – 3 = 8999993999998
299999992 – 3 = 899999939999998
122 – 3 = 141
1022 – 3 = 10401
10022 – 3 = 1004001
100022 – 3 = 100040001
1000022 – 3 = 10000400001
10000022 – 3 = 1000004000001
100000022 – 3 = 100000040000001

One finite palindromic pattern starting from length 15 !

281111102 – 3 = 790234505432097
2811111102 – 3 = 79023456165432097
28111111102 – 3 = 7902345672765432097
281111111102 – 3 = 790234567838765432097
2811111111102 – 3 = 79023456789498765432097

Four infinite palindromic pattern (probably more) hides in the list for case n^2 – 6

19132 – 6 = 3659563
190132 – 6 = 361494163
1900132 – 6 = 36104940163
19000132 – 6 = 3610049400163
190000132 – 6 = 361000494000163
1900000132 – 6 = 36100004940000163
1910872 – 6 = 36514241563
190109872 – 6 = 361417626714163
19001099872 – 6 = 3610417962697140163
1900010999872 – 6 = 36100417996269971400163
190000109999872 – 6 = 361000417999626999714000163
19000001099999872 – 6 = 3610000417999962699997140000163

This infinite palindromic pattern clean starting from length 19 !

19108913 [365150556041563] {L=15} Alas! Not palindromic but a NEAR MISS
19010890132 – 6 = 3614139435349314163 {L=19}
1900108900132 – 6 = 36104138323532383140163 {L=23}
190001089000132 – 6 = 361004138212353212831400163 {L=27}
19000010890000132 – 6 = 3610004138201235321028314000163 {L=31}
1900000108900000132 – 6 = 36100004138200123532100283140000163 {L=35}
190000001089000000132 – 6 = 361000004138200012353210002831400000163 {L=39}

This infinite palindromic pattern clean starting from length 25 !

1910989132 – 6 = 36518794549781563 {L=17}
19010989013 [361417703252406714163] {L=21} Alas! Not palindromic but a NEAR MISS
19001098900132 – 6 = 3610417594125214957140163 {L=25}
1900010989000132 – 6 = 36100417583212521238571400163 {L=29}
190000109890000132 – 6 = 361000417582121252121285714000163 {L=33}
19000001098900000132 – 6 = 3610000417582012125212102857140000163 {L=37}
1900000010989000000132 – 6 = 36100000417582001212521210028571400000163 {L=41}
190000000109890000000132 – 6 = 361000000417582000121252121000285714000000163 {L=45}
19000000001098900000000132 – 6 = 3610000000417582000012125212100002857140000000163 {L=49}
1900000000010989000000000132 – 6 = 36100000000417582000001212521210000028571400000000163 {L=53}

This finite (triplet) palindromic pattern clean starting from length 23 !

1901089109872 – 6 = 36141398036663089314163 {L=23}
190010891099872 – 6 = 361041387365666563783140163 {L=27}
19000108910999872 – 6 = 3610041386298566658926831400163 {L=31}

An infinite palindromic pattern hides in the list for case n^2 – 7

202 – 7 = 393
2002 – 7 = 39993
20002 – 7 = 3999993
200002 – 7 = 399999993
2000002 – 7 = 39999999993
20000002 – 7 = 3999999999993
200000002 – 7 = 399999999999993

A finite palindromic pattern with only four steps

1(63)2 – 7 = 26562
1(63)(63)2 – 7 = 267747762
1(63)(63)(63)2 – 7 = 2677683867762
1(63)(63)(63)(63)2 – 7 = 26776859295867762

Two infinite palindromic pattern hide in the list for case n^2 – 8

192 – 8 = 353
1992 – 8 = 39593
19992 – 8 = 3995993
199992 – 8 = 399959993
1999992 – 8 = 39999599993
19999992 – 8 = 3999995999993
199999992 – 8 = 399999959999993
132 – 8 = 161
1032 – 8 = 10601
10032 – 8 = 1006001
100032 – 8 = 100060001
1000032 – 8 = 10000600001
10000032 – 8 = 1000006000001
100000032 – 8 = 100000060000001


The Table


Index NrBasenumberLength
Palindromic Decremented Squares of form n^2–XLength
up down
[PG4] Case X = 0
See in-depth webpage about Palindromic Square Numbers
up down
[SD1] [QP2] Case X = 1
See in-depth webpage about Palindromic Quasipronic Numbers of the form n(n+2)
One can find the regular numbers of the form n2 – 1 at
%N n2 – 1 or n(n + 2). under A005563.
The palindromic numbers of the form n2 – 1 are categorised as follows :
%N n2 – 1 or n(n + 2) is a palindrome. under A028503.
%N Palindromes of the form n2 – 1 or n(n + 2). under A028504.

211
01
101
–11
up down
[SD2] Case X = 2
One can find the regular numbers of the form n2 – 2 at
%N n2 – 2. under A059100.
The palindromic numbers of the form n2 – 2 are categorised as follows :
%N n2 – 2 is a palindrome. under A0?????.
%N Palindromes of the form n2 – 2. under A0?????.

More terms from Robert Xiao, Nov 11, 2022. See Index Nrs 57 up to 64.
More terms from Robert Xiao, Dec 6, 2022. See Index Nrs 65 up to 78.
More terms from Patrick De Geest, Jun 20, 2023. See Index Nrs 79 up to 83.
More terms from Patrick De Geest, Jul 9, 2023. See Index Nrs 84 up to 87.
873.000.000.000.000.000.000.000.000.00028
8.999.999.999.999.999.999.999.999.999.999.999.999.999.999.999.999.999.99855
862.992.528.529.523.777.037.549.710.16028
8.955.227.000.013.739.296.679.566.204.026.659.766.929.373.100.007.225.59855
852.693.056.044.536.262.824.466.012.02328
7.252.550.859.013.301.617.488.987.319.137.898.847.161.033.109.580.552.52755
841.565.062.952.541.773.069.998.789.46228
2.449.422.045.418.772.224.786.334.203.024.336.874.222.778.145.402.249.44255
83315.861.171.273.312.886.868.863.40127
99.768.279.518.149.098.066.279.368.686.397.266.089.094.181.597.286.79953
82300.000.000.000.000.000.000.000.00027
89.999.999.999.999.999.999.999.999.999.999.999.999.999.999.999.999.99853
81179.620.570.276.574.319.648.943.21527
32.263.549.266.481.773.961.904.114.641.140.916.937.718.466.294.536.22353
80156.010.667.661.088.992.183.079.31227
24.339.328.424.058.758.670.718.634.743.681.707.685.785.042.482.393.34253
79142.247.231.721.150.292.162.588.30227
20.234.274.932.330.625.909.996.119.391.169.990.952.603.323.947.243.20253
7830.000.000.000.000.000.000.000.00026
899.999.999.999.999.999.999.999.999.999.999.999.999.999.999.999.99851
773.049.891.714.081.660.011.728.07125
9.301.839.467.623.966.182.275.841.485.722.816.693.267.649.381.03949
763.025.130.227.652.835.756.161.28925
9.151.412.894.258.897.887.886.028.206.887.887.988.524.982.141.51949
753.000.000.000.000.000.000.000.00025
8.999.999.999.999.999.999.999.999.999.999.999.999.999.999.999.99849
742.689.350.142.696.887.830.779.57325
7.232.604.190.023.770.937.815.885.885.187.390.773.200.914.062.32749
732.186.158.607.777.272.760.487.92425
4.779.289.458.358.663.520.258.802.088.520.253.668.538.549.829.77449
72300.000.000.000.000.000.000.00024
89.999.999.999.999.999.999.999.999.999.999.999.999.999.999.99847
71180.695.773.711.176.517.393.92524
32.650.962.637.080.710.605.658.485.650.601.708.073.626.905.62347
70179.508.816.227.708.121.396.33524
32.223.415.103.473.086.582.731.713.728.568.037.430.151.432.22347
69156.603.914.876.325.118.917.38824
24.524.786.154.591.283.885.902.520.958.838.219.545.168.742.54247
6830.000.000.000.000.000.000.00023
899.999.999.999.999.999.999.999.999.999.999.999.999.999.99845
6721.436.079.916.332.914.228.63423
459.505.522.179.411.319.076.454.670.913.114.971.225.505.95445
6615.667.408.990.634.221.076.88823
245.467.704.479.806.022.103.767.301.220.608.974.407.764.54245
6515.583.659.610.881.660.431.83823
242.850.446.867.824.344.223.515.322.443.428.768.644.058.24245
643.063.643.526.715.889.821.27922
9.385.911.658.788.175.109.093.909.015.718.878.561.195.83943
633.000.000.000.000.000.000.00022
8.999.999.999.999.999.999.999.999.999.999.999.999.999.99843
621.641.024.808.013.105.423.15822
2.692.962.420.514.449.513.043.403.159.444.150.242.692.96243
611.622.313.562.552.861.231.94222
2.631.901.295.242.956.393.272.723.936.592.425.921.091.36243
601.443.231.625.702.678.324.29822
2.082.917.525.428.395.785.151.515.875.938.245.257.192.80243
591.434.968.356.323.843.439.25222
2.059.134.183.650.752.911.354.531.192.570.563.814.319.50243
58300.000.000.000.000.000.00021
89.999.999.999.999.999.999.999.999.999.999.999.999.99841
57168.040.147.661.438.296.22221
28.237.491.226.077.986.494.649.468.977.062.219.473.28241
5630.000.000.000.000.000.00020
899.999.999.999.999.999.999.999.999.999.999.999.99839
5527.320.258.176.172.852.40720
746.396.506.812.739.591.747.195.937.218.605.693.64739
543.000.000.000.000.000.00019
8.999.999.999.999.999.999.999.999.999.999.999.99837
532.178.015.454.901.896.42619
4.743.751.321.791.514.824.284.151.971.231.573.47437
521.509.542.387.634.560.58219
2.278.718.220.065.449.960.699.445.600.228.178.72237
51300.000.000.000.000.00018
89.999.999.999.999.999.999.999.999.999.999.99835
50277.046.141.819.110.63718
76.754.564.696.854.763.736.745.869.646.545.76735
49167.724.793.753.032.07218
28.131.606.439.497.146.364.179.493.460.613.18235
48163.836.377.167.092.80818
26.842.358.483.237.889.598.873.238.485.324.86235
4730.000.000.000.000.00017
899.999.999.999.999.999.999.999.999.999.99833
4626.864.628.003.947.87717
721.708.237.790.500.494.005.097.732.807.12733
453.057.109.285.491.27116
9.345.917.183.436.949.496.343.817.195.43931
443.000.000.000.000.00016
8.999.999.999.999.999.999.999.999.999.99831
432.997.152.982.455.77016
8.982.926.000.243.517.153.420.006.292.89831
42300.000.000.000.00015
89.999.999.999.999.999.999.999.999.99829
41151.051.744.377.76815
22.816.629.479.566.566.597.492.661.82229
4030.000.000.000.00014
899.999.999.999.999.999.999.999.99827
393.000.000.000.00013
8.999.999.999.999.999.999.999.99825
382.736.719.294.29313
7.489.632.495.755.575.942.369.84725
371.434.419.498.75213
2.057.559.298.399.938.929.557.50225
36300.000.000.00012
89.999.999.999.999.999.999.99823
35277.104.474.86312
76.786.889.989.098.998.868.76723
34169.944.971.37812
28.881.293.296.669.239.218.88223
33150.408.075.56812
22.622.589.196.069.198.522.62223
3230.000.000.00011
899.999.999.999.999.999.99821
3120.470.241.05411
419.030.768.808.867.030.91421
3020.414.740.29611
416.761.621.353.126.167.61421
2920.371.679.75411
415.005.335.999.533.500.51421
283.000.000.00010
8.999.999.999.999.999.99819
272.759.060.76310
7.612.416.293.926.142.16719
262.728.091.60710
7.442.483.816.183.842.44719
251.807.133.72510
3.265.732.300.032.375.62319
241.489.076.31810
2.217.348.280.828.437.12219
23314.838.8999
99.123.532.323.532.19917
22300.000.0009
89.999.999.999.999.99817
2130.000.0008
899.999.999.999.99815
2020.367.6968
414.843.040.348.41415
193.000.0007
8.999.999.999.99813
18300.0006
89.999.999.99811
17202.5046
41.007.870.01411
16151.2326
22.871.117.82211
15144.2986
20.821.912.80211
1430.0005
899.999.9989
133.1494
Prime!    9.916.1997
123.0004
8.999.9987
112.1744
4.726.2747
102.0944
4.384.8347
93003
89.9985
82043
41.6145
7Prime!    312
9593
6302
8983
5272
Prime!    7273
4Prime!    31
Prime!    71
3Prime!    21
Prime!    21
211
–11
101
–21
up down
[SD3] Case X = 3
One can find the regular numbers of the form n2 – 3 at
%N n2 – 3. under A028872.
The palindromic numbers of the form n2 – 3 are categorised as follows :
%N n2 – 3 is a palindrome. under A0?????.
%N Palindromes of the form n2 – 3. under A0?????.

More terms from Robert Xiao, Nov 11, 2022. See Index Nrs 115 up to 145.
More terms from Robert Xiao, Dec 6, 2022. See Index Nrs 146 up to 171.
More terms from Robert Xiao, Jun 20, 2023. See Index Nrs 172 up to 175.
More terms from Patrick De Geest, Jul 9, 2023. See Index Nrs 176 up to 182.
1822.999.999.999.999.999.999.999.999.99928
8.999.999.999.999.999.999.999.999.993.999.999.999.999.999.999.999.999.99855
1811.821.400.107.671.155.042.475.937.94428
3.317.498.352.224.495.181.808.974.923.294.798.081.815.944.222.538.947.13355
1801.295.938.605.931.335.905.464.552.95828
1.679.456.870.343.254.334.095.675.843.485.765.904.334.523.430.786.549.76155
1791.133.608.238.191.781.334.320.568.23228
1.285.067.637.696.274.444.997.636.641.466.367.994.444.726.967.367.605.82155
1781.000.000.000.000.000.000.000.000.00228
1.000.000.000.000.000.000.000.000.004.000.000.000.000.000.000.000.000.00155
177471.308.194.139.797.273.796.334.71527
222.131.413.863.316.837.297.691.354.453.196.792.738.613.368.314.131.22254
176352.646.444.960.705.941.761.799.13227
124.359.515.143.424.205.106.895.024.420.598.601.502.424.341.515.953.42154
175299.999.999.999.999.999.999.999.99926
89.999.999.999.999.999.999.999.999.399.999.999.999.999.999.999.999.99853
174295.094.367.852.435.585.719.224.75926
87.080.685.938.228.568.878.824.167.776.142.887.886.582.283.958.608.07853
173258.298.697.590.425.346.638.181.61326
66.718.217.176.910.004.773.433.372.127.333.437.740.001.967.171.281.76653
172100.000.000.000.000.000.000.000.00227
10.000.000.000.000.000.000.000.000.400.000.000.000.000.000.000.000.00153
17129.999.999.999.999.999.999.999.99926
899.999.999.999.999.999.999.999.939.999.999.999.999.999.999.999.99851
17014.914.134.380.859.994.636.898.93526
222.431.404.330.350.135.562.319.636.913.265.531.053.033.404.134.22251
16913.566.414.879.344.120.953.647.52226
184.047.612.678.489.559.892.597.242.795.298.955.984.876.216.740.48151
16810.960.288.120.601.689.757.894.96826
120.127.915.686.602.520.611.125.818.521.116.025.206.686.519.721.02151
16710.264.737.038.759.668.003.975.25226
105.364.826.474.884.598.038.553.696.355.830.895.488.474.628.463.50151
16610.065.373.554.200.832.189.772.65226
101.311.744.785.605.492.939.499.454.994.939.294.506.587.447.113.10151
16510.000.000.000.000.000.000.000.00226
100.000.000.000.000.000.000.000.040.000.000.000.000.000.000.000.00151
1648.905.093.612.821.384.449.884.98025
79.300.692.253.112.217.380.008.411.480.008.371.221.135.229.600.39750
1633.846.171.129.314.339.239.057.08825
14.793.032.355.971.139.653.045.211.254.035.693.117.955.323.039.74150
1622.999.999.999.999.999.999.999.99925
8.999.999.999.999.999.999.999.993.999.999.999.999.999.999.999.99849
1612.811.479.238.955.891.088.405.21025
7.904.415.511.079.996.542.594.668.664.952.456.999.701.155.144.09749
1602.582.669.819.005.597.932.591.86325
6.670.183.394.002.407.984.107.633.367.014.897.042.004.933.810.76649
1591.817.883.077.221.740.239.997.00625
3.304.698.882.449.183.588.610.120.210.168.853.819.442.888.964.03349
1581.000.000.000.000.000.000.000.00225
1.000.000.000.000.000.000.000.004.000.000.000.000.000.000.000.00149
157299.999.999.999.999.999.999.99924
89.999.999.999.999.999.999.999.399.999.999.999.999.999.999.99847
156128.166.476.869.721.072.893.59224
Prime!    16.426.645.793.196.746.787.836.363.878.764.769.139.754.662.46147
155112.032.177.277.987.708.325.71824
12.551.208.745.646.465.363.219.591.236.356.464.654.780.215.52147
154100.000.000.000.000.000.000.00224
10.000.000.000.000.000.000.000.400.000.000.000.000.000.000.00147
15390.100.051.300.112.592.414.01123
8.118.019.244.282.920.854.556.776.554.580.292.824.429.108.11846
15281.681.408.051.585.923.231.61323
6.671.852.421.289.685.687.737.227.377.865.869.821.242.581.76646
15129.999.999.999.999.999.999.99923
899.999.999.999.999.999.999.939.999.999.999.999.999.999.99845
15025.803.748.116.971.259.068.41323
665.833.416.884.097.798.170.363.071.897.790.488.614.338.56645
14919.790.203.234.598.368.535.48623
391.652.144.066.707.728.608.555.806.827.707.660.441.256.19345
14819.245.315.697.612.922.546.27423
370.382.176.300.786.371.611.080.116.173.687.003.671.283.07345
14715.052.541.436.309.324.841.72523
226.579.003.691.809.192.090.595.090.291.908.196.300.975.62245
14610.000.000.000.000.000.000.00223
100.000.000.000.000.000.000.040.000.000.000.000.000.000.00145
1458.920.703.636.328.181.721.26022
79.578.953.367.198.844.244.333.344.244.889.176.335.987.59744
1444.715.440.199.567.243.058.11522
22.235.376.275.694.761.039.000.093.016.749.657.267.353.22244
1432.999.999.999.999.999.999.99922
8.999.999.999.999.999.999.993.999.999.999.999.999.999.99843
1422.932.281.979.085.269.674.71922
8.598.277.604.868.225.902.074.702.095.228.684.067.728.95843
1412.455.312.313.348.022.525.95322
6.028.558.556.078.417.955.468.645.597.148.706.558.558.20643
1401.781.373.349.799.351.637.34622
3.173.291.011.375.363.208.134.318.023.635.731.101.923.71343
1391.485.796.241.775.497.674.54522
2.207.590.472.074.193.141.087.801.413.914.702.740.957.02243
1381.126.087.189.632.135.564.06822
1.268.072.358.653.601.242.216.122.421.063.568.532.708.62143
1371.000.000.000.000.000.000.00222
1.000.000.000.000.000.000.004.000.000.000.000.000.000.00143
136582.838.484.258.758.474.54421
339.700.698.733.047.050.117.711.050.740.337.896.007.93342
135299.999.999.999.999.999.99921
89.999.999.999.999.999.999.399.999.999.999.999.999.99841
134Prime!    298.662.980.564.353.438.35121
89.199.575.959.583.359.660.806.695.338.595.957.599.19841
133281.083.978.194.149.098.49021
79.008.202.797.448.885.895.059.858.884.479.720.280.09741
132257.900.049.025.073.457.66321
66.512.435.287.135.292.920.402.929.253.178.253.421.56641
131254.693.803.297.861.396.20721
64.868.933.438.329.712.622.422.621.792.383.433.986.84641
130111.759.696.530.330.271.86821
12.490.229.768.551.516.208.380.261.515.586.792.209.42141
129100.000.000.000.000.000.00221
10.000.000.000.000.000.000.400.000.000.000.000.000.00141
12856.394.005.800.121.742.39620
3.180.283.890.184.164.722.772.274.614.810.983.820.81340
12735.995.428.476.577.544.61820
1.295.670.871.212.409.614.554.169.042.121.780.765.92140
126Prime!    29.999.999.999.999.999.99920
899.999.999.999.999.999.939.999.999.999.999.999.99839
12529.997.253.737.690.261.74920
899.835.231.803.372.378.828.873.273.308.132.538.99839
12429.177.676.372.510.968.13120
851.336.798.498.984.807.909.708.489.894.897.633.15839
12317.803.641.833.835.566.20420
316.969.662.547.499.842.737.248.994.745.266.969.61339
12210.000.000.000.000.000.00220
100.000.000.000.000.000.040.000.000.000.000.000.00139
1213.582.587.753.716.697.73219
12.834.935.013.080.854.044.045.808.031.053.943.82138
1202.999.999.999.999.999.99919
8.999.999.999.999.999.993.999.999.999.999.999.99837
1192.825.751.166.471.612.07019
7.984.869.654.815.676.269.626.765.184.569.684.89737
1181.945.547.844.192.374.87419
3.785.156.414.041.597.378.737.951.404.146.515.87337
1171.776.625.653.788.234.25419
3.156.398.713.698.470.802.080.748.963.178.936.51337
1161.037.382.092.965.871.44819
1.076.161.606.806.251.951.591.526.086.061.616.70137
1151.000.000.000.000.000.00219
1.000.000.000.000.000.004.000.000.000.000.000.00137
114800.096.871.932.978.49318
640.155.004.476.936.987.789.639.674.400.551.04636
113432.342.232.793.964.32218
186.919.806.257.270.438.834.072.752.608.919.68136
112299.999.999.999.999.99918
89.999.999.999.999.999.399.999.999.999.999.99835
111250.947.643.580.916.82718
62.974.719.818.814.866.366.841.881.891.747.92635
110129.576.704.573.474.54218
16.790.122.368.121.498.289.412.186.322.109.76135
109112.894.940.866.782.08218
12.745.267.673.314.223.032.241.337.676.254.72135
108100.000.000.000.000.00218
10.000.000.000.000.000.400.000.000.000.000.00135
10737.831.729.891.151.31217
1.431.239.786.557.031.661.307.556.879.321.34134
10629.999.999.999.999.99917
899.999.999.999.999.939.999.999.999.999.99833
10510.000.000.000.000.00217
100.000.000.000.000.040.000.000.000.000.00133
1043.813.173.873.483.11216
14.540.294.989.414.200.241.498.949.204.54132
1033.225.129.724.100.10216
10.401.461.737.274.000.047.273.716.410.40132
1023.213.817.208.205.04816
10.328.621.047.754.888.845.774.012.682.30132
1012.999.999.999.999.99916
8.999.999.999.999.993.999.999.999.999.99831
1002.859.912.361.666.81116
8.179.098.716.414.636.364.146.178.909.71831
991.984.826.623.628.58616
3.939.536.725.864.852.584.685.276.359.39331
981.975.077.481.649.56416
3.900.931.058.519.183.819.158.501.390.09331
971.363.557.307.075.17216
1.859.288.529.678.094.908.769.258.829.58131
961.104.380.147.463.31816
1.219.655.510.111.100.011.110.155.569.12131
951.000.000.000.000.00216
1.000.000.000.000.004.000.000.000.000.00131
94925.076.769.015.58115
855.767.028.572.306.603.275.820.767.55830
93793.326.228.722.92315
629.366.505.179.735.537.971.505.663.92630
92299.999.999.999.99915
89.999.999.999.999.399.999.999.999.99829
91257.617.848.652.46315
66.366.955.944.323.332.344.955.966.36629
90187.685.767.311.01615
35.225.947.251.124.842.115.274.952.25329
89177.196.446.108.35415
31.398.580.513.430.803.431.508.589.31329
88111.009.388.950.48215
12.323.084.435.159.395.153.448.032.32129
87100.000.000.000.00215
10.000.000.000.000.400.000.000.000.00129
8629.999.999.999.99914
899.999.999.999.939.999.999.999.99827
8528.927.607.042.87914
836.806.449.227.222.722.944.608.63827
8418.401.474.433.90614
338.614.261.341.696.143.162.416.83327
8315.052.520.152.52514
226.578.362.942.171.249.263.875.62227
8214.843.663.905.69514
220.334.358.145.232.541.853.433.02227
8111.982.083.209.81214
143.570.318.046.858.640.813.075.34127
8010.000.000.000.00214
100.000.000.000.040.000.000.000.00127
796.108.627.042.87613
37.315.324.348.955.984.342.351.37326
784.700.308.259.34513
22.092.897.732.866.823.779.829.02226
772.999.999.999.99913
8.999.999.999.993.999.999.999.99825
762.542.454.379.84313
6.464.074.273.582.853.724.704.64625
751.108.553.389.83213
1.228.890.618.108.018.160.988.22125
741.000.000.000.00213
1.000.000.000.004.000.000.000.00125
73299.999.999.99912
89.999.999.999.399.999.999.99823
72298.530.039.85112
89.120.184.693.439.648.102.19823
71293.254.640.78112
85.998.284.339.593.348.289.95823
70281.111.111.11012
79.023.456.789.498.765.432.09723
69149.088.589.58512
22.227.407.544.444.570.472.22223
68134.952.824.27812
Prime!    18.212.264.780.608.746.221.28123
67100.000.000.00212
10.000.000.000.400.000.000.00123
6638.318.240.26211
1.468.287.536.776.357.828.64122
6529.999.999.99911
899.999.999.939.999.999.99821
6428.111.111.11011
790.234.567.838.765.432.09721
6310.145.537.69811
102.931.935.181.539.139.20121
6210.000.000.00211
100.000.000.040.000.000.00121
615.748.742.99410
33.048.046.011.064.084.03320
602.999.999.99910
8.999.999.993.999.999.99819
592.811.111.11010
7.902.345.672.765.432.09719
582.578.854.58710
6.650.490.980.890.940.56619
571.485.275.39510
2.206.042.998.992.406.02219
561.104.201.68210
Prime!    1.219.261.354.531.629.12119
551.038.329.05210
1.078.127.220.227.218.70119
541.000.000.00210
1.000.000.004.000.000.00119
53299.999.9999
89.999.999.399.999.99817
52281.111.1109
79.023.456.165.432.09717
51198.699.8649
39.481.635.953.618.49317
50119.193.8389
14.207.171.017.170.24117
49100.000.0029
10.000.000.400.000.00117
4892.274.8818
8.514.653.663.564.15816
4759.963.8668
3.595.665.225.665.95316
4643.535.7728
1.895.363.443.635.98116
45Prime!    29.999.9998
899.999.939.999.99815
4428.111.1108
790.234.505.432.09715
4324.544.2978
602.422.515.224.20615
4218.750.5348
351.582.525.285.15315
4110.000.0028
100.000.040.000.00115
409.260.0697
85.748.877.884.75814
399.258.4317
85.718.544.581.75814
388.157.9137
66.551.544.515.56614
373.563.9187
12.701.511.510.72114
363.281.4487
10.767.900.976.70114
35Prime!    2.999.9997
8.999.993.999.99813
341.484.8457
2.204.764.674.02213
331.000.0027
1.000.004.000.00113
32889.1906
790.658.856.09712
31299.9996
89.999.399.99811
30Prime!    249.3776
62.188.888.12611
29150.5256
22.657.775.62211
28148.5056
22.053.735.02211
27100.0026
10.000.400.00111
2689.3705
7.986.996.89710
2579.3275
6.292.772.92610
2442.8725
1.838.008.38110
2340.9585
1.677.557.76110
2240.4425
1.635.555.36110
2129.9995
899.939.9989
20Prime!    24.5475
602.555.2069
1912.9585
167.909.7619
1811.8625
140.707.0419
1710.0025
100.040.0019
16Prime!    2.9994
8.993.9987
151.8844
3.549.4537
141.0024
1.004.0017
132993
89.3985
121023
10.4015
11Prime!    832
6.8864
10382
1.4414
9Prime!    292
8383
8152
2223
7122
1413
661
332
5Prime!    51
222
4Prime!    31
61
3Prime!    21
11
211
–21
101
–31
up down
[SD4] [QP4] Case X = 4
See in-depth webpage about Palindromic Quasipronic Numbers of the form n(n+4)
One can find the regular numbers of the form n2 – 4 at
%N n2 – 4 or n(n+4). under A028347.
The palindromic numbers of the form n2 – 4 are categorised as follows :
%N n2 – 4 or n(n+4) is a palindrome. under A028555.
%N Palindromes of the form n2 – 4 or n(n+4). under A028556.
211
–31
101
–41
up down
[SD5] Case X = 5
One can find the regular numbers of the form n2 – 5 at
%N n2 – 5. under A028875.
The palindromic numbers of the form n2 – 5 are categorised as follows :
%N n2 – 5 is a palindrome. under A0?????.
%N Palindromes of the form n2 – 5. under A0?????.

More terms from Robert Xiao, Nov 11, 2022. See Index Nrs 71 up to 89.
More terms from Robert Xiao, Dec 6, 2022. See Index Nrs 90 up to 105.
More terms from Patrick De Geest, Jun 20, 2023. See Index Nrs 106 up to 111.
More terms from Patrick De Geest, Jul 9, 2023. See Index Nrs 112 up to 115.
1152.636.341.652.101.597.022.921.990.94928
6.950.297.306.605.778.030.507.208.926.298.027.050.308.775.066.037.920.59655
1142.446.222.381.131.255.171.465.049.93028
5.984.003.937.947.467.837.136.823.316.133.286.317.387.647.497.393.004.89555
1132.057.723.754.261.793.051.377.720.32328
4.234.227.048.853.248.076.972.690.671.760.962.796.708.423.588.407.224.32455
112806.849.572.103.352.092.030.152.88127
651.006.232.003.362.366.450.348.581.185.843.054.663.263.300.232.600.15654
111306.417.893.480.358.089.137.021.56227
93.891.925.444.940.076.348.488.564.446.588.484.367.004.944.452.919.83953
110303.233.785.842.546.894.744.602.88227
91.950.728.876.403.593.576.690.350.305.309.667.539.530.467.882.705.91953
109247.272.683.196.670.359.099.446.73927
61.143.779.855.280.903.760.866.548.084.566.806.730.908.255.897.734.11653
108130.933.676.892.235.472.836.866.77627
17.143.627.744.520.317.428.342.369.596.324.382.471.302.544.772.634.17153
107108.823.449.026.472.802.033.104.39627
11.842.543.058.017.324.244.574.074.347.047.544.242.371.085.034.524.81153
106107.962.166.475.168.632.075.545.70427
11.655.829.390.012.025.694.051.208.580.215.049.652.021.009.392.855.61153
10598.706.372.344.366.291.811.755.52226
9.742.947.941.384.678.726.251.531.991.351.526.278.764.831.497.492.47952
10430.899.910.999.009.009.989.100.09226
954.804.499.746.677.993.723.589.686.985.327.399.776.647.994.408.45951
10325.601.533.666.146.599.823.394.08126
655.438.526.058.837.760.184.127.929.721.481.067.738.850.625.834.55651
10214.046.857.898.295.232.233.356.21426
197.314.216.814.899.148.861.814.989.418.168.841.998.418.612.413.79151
10110.796.935.780.449.746.834.514.29626
116.573.822.247.155.983.779.220.555.022.977.389.551.742.228.375.61151
10010.576.014.188.239.189.379.931.95426
111.852.076.109.836.639.895.615.747.516.598.936.638.901.670.258.11151
99694.639.323.223.772.025.418.73324
482.523.789.368.780.025.536.488.884.635.520.087.863.987.325.28448
98335.436.596.236.559.381.705.59624
112.517.710.094.768.563.558.339.933.855.365.867.490.017.715.21148
97309.756.178.646.877.050.585.15824
95.948.890.209.916.010.068.792.329.786.001.061.990.209.884.95947
96302.732.470.814.007.788.860.06824
91.646.948.885.154.077.704.302.420.340.777.045.158.884.964.61947
95206.699.971.468.848.284.423.02724
42.724.878.205.222.694.807.097.579.070.849.622.250.287.842.72447
94200.167.952.251.948.320.953.99724
40.067.209.108.738.262.893.878.487.839.826.283.780.190.276.00447
93139.529.692.368.665.263.905.86424
19.468.535.052.494.365.583.681.918.638.556.349.425.053.586.49147
9269.725.233.830.223.544.465.86723
4.861.608.232.679.349.849.208.008.029.489.439.762.328.061.68446
9139.309.749.032.806.409.291.11623
1.545.256.369.022.224.430.726.336.270.344.222.209.636.525.45146
9037.266.967.598.077.420.372.59423
1.388.826.873.956.152.334.637.777.364.332.516.593.786.288.83146
893.085.728.226.186.532.441.79222
9.521.718.685.884.283.917.439.347.193.824.885.868.171.25943
882.568.526.826.754.912.388.53122
6.597.330.059.759.659.719.013.109.179.569.579.500.337.95643
872.157.873.004.828.956.120.16322
4.656.415.904.969.548.083.087.803.808.459.694.095.146.56443
861.408.572.019.246.858.638.66422
1.984.075.133.405.172.703.202.023.072.715.043.315.704.89143
85695.915.206.770.872.717.93321
484.297.975.014.946.529.194.491.925.649.410.579.792.48442
84263.361.890.200.005.602.70121
69.359.485.209.719.807.115.851.170.891.790.258.495.39641
83260.419.908.473.754.958.85921
67.818.528.729.478.909.825.652.890.987.492.782.581.87641
82243.687.672.804.575.076.28021
59.383.681.876.909.639.223.132.293.690.967.818.638.39541
81107.935.634.905.637.141.79621
11.650.101.282.482.994.967.576.949.928.428.210.105.61141
8096.601.787.108.181.943.81220
9.331.905.272.494.507.198.448.917.054.942.725.091.33940
7980.834.098.973.624.803.01920
6.534.151.556.877.770.432.882.340.777.786.551.514.35640
7834.112.245.172.201.928.29620
1.163.645.270.688.413.764.664.673.148.860.725.463.61140
7726.448.681.811.466.663.24920
699.532.769.564.207.495.292.594.702.465.967.235.99639
7625.924.938.851.309.967.84120
672.102.454.444.160.994.848.499.061.444.454.201.27639
7512.302.681.654.262.901.53420
151.355.975.886.136.963.474.369.631.688.579.553.15139
749.591.559.188.295.808.88219
91.998.007.662.581.756.144.165.718.526.670.089.91938
736.508.812.195.058.877.32319
42.364.636.190.547.160.900.906.174.509.163.646.32438
723.052.350.428.958.801.51219
9.316.843.141.164.979.595.959.794.611.413.486.13937
711.067.246.203.069.548.35419
1.139.014.457.966.367.642.467.636.697.544.109.31137
70682.169.346.558.220.91318
465.355.017.383.670.106.601.076.383.710.553.56436
6997.596.148.796.869.70817
9.525.008.259.980.732.552.370.899.528.005.25934
6825.141.809.369.422.57917
632.110.578.368.384.979.483.863.875.011.23633
6711.794.718.752.417.45617
139.115.390.448.627.989.726.844.093.511.93133
663.147.974.405.060.84816
9.909.742.854.918.199.918.194.582.479.09931
653.060.109.141.231.76216
9.364.267.956.250.191.910.526.597.624.63931
642.480.391.882.989.53916
6.152.343.893.200.390.930.023.983.432.51631
631.177.345.302.316.09416
1.386.141.960.885.774.775.880.691.416.83131
62835.457.574.010.09915
697.989.357.970.840.048.079.753.989.79630
61370.527.710.594.14415
137.290.784.318.137.731.813.487.092.73130
60367.286.418.313.20615
134.899.313.077.343.343.770.313.998.43130
59311.724.544.575.57215
97.172.191.690.847.774.809.619.127.17929
58202.050.838.683.80315
40.824.541.412.828.182.821.414.542.80429
5797.888.964.408.30814
9.582.249.352.930.990.392.539.422.85928
56Prime!    79.518.245.402.17114
6.323.151.351.839.889.381.531.513.23628
5524.376.775.668.35014
594.227.191.985.060.589.191.722.49527
5420.991.089.109.00714
440.625.821.982.272.289.128.526.04427
5312.583.404.092.31614
158.342.058.550.515.055.850.243.85127
526.851.026.560.06313
46.936.564.926.688.662.946.563.96426
513.055.742.940.31213
9.337.564.917.266.627.194.657.33925
502.108.821.814.64313
4.447.129.445.914.195.449.217.44425
49682.055.723.83712
465.200.010.418.814.010.002.56424
48315.458.954.59812
99.514.352.036.063.025.341.59923
47309.549.710.80812
95.821.023.461.316.432.012.85923
46303.103.448.76812
91.871.700.655.055.600.717.81923
45251.972.689.52112
63.490.236.264.446.263.209.43623
44209.910.890.99312
44.062.582.157.475.128.526.04423
43140.638.946.71412
19.779.313.332.823.331.397.79123
42131.073.116.27612
17.180.161.810.301.816.108.17123
4198.841.904.32211
9.769.722.049.999.402.279.67922
4079.408.330.07111
6.305.682.884.664.882.865.03622
3931.283.616.87811
978.664.684.969.486.466.87921
3830.629.582.06211
938.171.297.292.792.171.83921
3724.849.903.93911
617.517.725.777.527.715.71621
3624.468.311.87011
598.698.285.767.582.896.89521
3520.990.990.99311
440.621.702.868.207.126.04421
3412.252.321.91611
150.119.392.333.293.911.05121
337.820.800.73910
61.164.924.199.142.946.11620
323.092.785.89210
9.565.324.573.754.235.65919
312.435.714.18010
5.932.703.566.653.072.39519
302.099.109.00710
4.406.258.623.268.526.04419
291.397.314.18610
1.952.486.934.396.842.59119
281.053.649.04610
1.110.176.312.136.710.11119
27210.900.8939
44.479.186.668.197.44417
2664.942.1238
4.217.479.339.747.12416
2521.089.1078
444.750.434.057.44415
2420.990.9938
440.621.787.126.04415
232.628.8517
6.910.857.580.19613
222.436.4207
5.936.142.416.39513
21978.5426
957.544.445.75912
20Prime!    783.3616
613.654.456.31612
19252.3796
63.695.159.63611
18210.8936
44.475.857.44411
1777.3705
5.986.116.89510
1669.4835
4.827.887.28410
15Prime!    21.6135
467.121.7649
1410.6965
114.404.4119
133.6564
13.366.3318
122.4404
5.953.5957
111.1564
1.336.3317
104363
190.0916
92593
67.0765
8812
6.5564
7142
Prime!    1913
6Prime!    71
442
541
Prime!    112
4Prime!    31
41
3Prime!    21
–11
211
–41
101
–51
up down
[SD6] Case X = 6
One can find the regular numbers of the form n2 – 6 at
%N n2 – 6. under A028878.
The palindromic numbers of the form n2 – 6 are categorised as follows :
%N n2 – 6 is a palindrome. under A0?????.
%N Palindromes of the form n2 – 6. under A0?????.

More terms from Robert Xiao, Nov 11, 2022. See Index Nrs 70 up to 105.
More terms from Robert Xiao, Dec 6, 2022. See Index Nrs 106 up to 144.
More terms from Patrick De Geest, Jun 20, 2023. See Index Nrs 145 up to 155.
More terms from Patrick De Geest, Jul 9, 2023. See Index Nrs 156 up to 174.
1742.989.001.099.998.910.999.989.001.10228
8.934.127.575.794.699.955.538.449.749.479.448.355.599.964.975.757.214.39855
1732.989.001.099.989.001.099.989.001.10228
8.934.127.575.735.458.551.536.789.539.359.876.351.558.545.375.757.214.39855
1722.989.000.001.090.090.089.000.001.10228
8.934.121.006.516.558.553.230.302.989.892.030.323.558.556.156.001.214.39855
1712.959.049.561.906.601.130.065.501.67228
8.755.974.309.819.648.073.666.778.856.588.776.663.708.469.189.034.795.57855
1702.955.132.134.183.155.857.922.823.62828
8.732.805.930.481.893.478.589.695.258.525.969.858.743.981.840.395.082.37855
1692.275.677.208.288.553.433.075.162.56128
5.178.706.756.323.984.205.961.864.665.664.681.695.024.893.236.576.078.71555
1682.232.958.924.971.439.437.357.687.63028
4.986.105.560.609.606.498.490.469.727.279.640.948.946.069.060.655.016.89455
1672.225.625.684.366.856.089.191.832.94028
4.953.409.686.913.436.525.008.859.778.779.588.005.256.343.196.869.043.59455
1661.966.116.804.908.224.745.186.928.11728
3.865.615.290.542.526.283.466.147.171.717.416.643.826.252.450.925.165.68355
1651.900.000.109.998.910.999.890.000.01328
3.610.000.417.995.873.899.342.421.211.121.242.439.983.785.997.140.000.16355
1641.900.000.109.989.001.099.890.000.01328
3.610.000.417.958.216.277.162.363.001.003.632.617.726.128.597.140.000.16355
1631.900.000.010.999.890.001.099.999.98728
3.610.000.041.799.582.125.177.579.986.899.757.715.212.859.971.400.000.16355
1621.900.000.010.890.000.108.900.000.01328
3.610.000.041.382.000.532.412.102.421.242.012.142.350.002.831.400.000.16355
1611.900.000.001.099.999.989.000.000.01328
3.610.000.004.179.999.959.410.000.025.200.000.149.599.999.714.000.000.16355
160Prime!    1.900.000.000.109.999.890.000.000.01328
3.610.000.000.417.999.582.012.100.025.200.012.102.859.997.140.000.000.16355
1591.900.000.000.010.998.900.000.000.01328
3.610.000.000.041.795.820.000.121.025.201.210.000.285.971.400.000.000.16355
1581.900.000.000.001.089.000.000.000.01328
3.610.000.000.004.138.200.000.001.235.321.000.000.028.314.000.000.000.16355
1571.900.000.000.000.109.999.999.999.98728
3.610.000.000.000.417.999.999.999.962.699.999.999.997.140.000.000.000.16355
1561.900.000.000.000.000.000.000.000.01328
3.610.000.000.000.000.000.000.000.049.400.000.000.000.000.000.000.000.16355
155298.900.109.989.099.109.989.001.10227
89.341.275.751.495.545.553.347.885.758.874.335.554.559.415.757.214.39853
154298.900.010.890.000.010.890.001.10227
89.341.216.510.042.125.102.142.895.959.824.120.152.124.001.561.214.39853
153286.211.070.762.787.459.902.955.61827
81.916.777.027.181.330.744.658.756.165.785.644.703.318.172.077.761.91853
152285.618.951.352.031.336.378.134.78227
81.578.185.371.434.043.154.828.053.335.082.845.134.043.417.358.187.51853
151223.309.951.952.607.124.808.663.87027
49.867.334.641.075.702.634.007.560.606.570.043.620.757.014.643.376.89453
150190.000.010.998.901.099.890.000.01327
36.100.004.179.582.538.934.025.410.101.452.043.983.528.597.140.000.16353
149190.000.010.989.000.109.890.000.01327
36.100.004.175.820.162.516.323.420.102.432.361.526.102.857.140.000.16353
148190.000.000.109.999.989.000.000.01327
36.100.000.041.799.995.832.100.002.520.000.123.859.999.714.000.000.16353
147190.000.000.010.999.890.000.000.01327
36.100.000.004.179.958.200.121.002.520.012.100.285.997.140.000.000.16353
146190.000.000.001.098.900.000.000.01327
36.100.000.000.417.582.000.001.212.521.210.000.028.571.400.000.000.16353
145190.000.000.000.000.000.000.000.01327
36.100.000.000.000.000.000.000.004.940.000.000.000.000.000.000.000.16353
14430.273.893.084.373.482.135.352.07526
916.508.602.484.076.547.525.004.959.400.525.745.670.484.206.805.61951
14329.890.010.900.899.909.910.998.89826
893.412.751.655.915.444.098.360.020.063.890.444.519.556.157.214.39851
14229.624.493.896.962.408.194.911.02826
877.610.638.651.162.970.208.130.484.031.802.079.261.156.836.016.77851
14122.360.242.318.400.148.405.890.30026
499.980.436.537.572.843.761.897.171.798.167.348.275.735.634.089.99451
14019.000.010.999.891.099.989.000.01326
361.000.417.995.982.797.186.212.111.212.681.797.289.599.714.000.16351
13919.000.010.998.900.109.989.000.01326
361.000.417.958.325.155.385.630.010.036.583.551.523.859.714.000.16351
13819.000.001.099.989.000.109.999.98726
361.000.041.799.583.214.155.799.868.997.551.412.385.997.140.000.16351
13719.000.001.098.900.109.890.000.01326
361.000.041.758.205.383.401.452.010.254.104.383.502.857.140.000.16351
136Prime!    19.000.000.109.989.001.099.999.98726
361.000.004.179.582.053.897.579.868.975.798.350.285.971.400.000.16351
13519.000.000.010.999.989.000.000.01326
361.000.000.417.999.582.121.000.252.000.121.285.999.714.000.000.16351
13419.000.000.001.099.890.000.000.01326
361.000.000.041.795.820.001.210.252.012.100.028.597.140.000.000.16351
13319.000.000.000.108.900.000.000.01326
361.000.000.004.138.200.000.012.353.210.000.002.831.400.000.000.16351
13219.000.000.000.010.999.999.999.98726
361.000.000.000.417.999.999.999.626.999.999.999.714.000.000.000.16351
13119.000.000.000.000.000.000.000.01326
361.000.000.000.000.000.000.000.494.000.000.000.000.000.000.000.16351
1302.279.376.050.249.040.746.865.16125
5.195.555.178.448.917.527.819.142.419.187.257.198.448.715.555.91549
1291.961.796.586.024.792.052.652.31725
3.848.645.844.938.529.324.507.110.117.054.239.258.394.485.468.48349
1281.902.617.477.488.931.470.344.73725
3.619.953.265.646.344.650.305.461.645.030.564.436.465.623.599.16349
1271.900.001.099.890.109.989.000.01325
3.610.004.179.583.627.716.454.101.014.546.177.263.859.714.000.16349
1261.900.000.108.900.010.890.000.01325
3.610.000.413.820.053.241.212.421.242.121.423.500.283.140.000.16349
1251.900.000.010.999.998.900.000.01325
3.610.000.041.799.995.941.000.025.200.001.495.999.971.400.000.16349
1241.900.000.001.099.989.000.000.01325
3.610.000.004.179.958.201.210.025.200.121.028.599.714.000.000.16349
1231.900.000.000.109.890.000.000.01325
3.610.000.000.417.582.000.012.125.212.100.002.857.140.000.000.16349
1221.900.000.000.000.000.000.000.01325
3.610.000.000.000.000.000.000.049.400.000.000.000.000.000.000.16349
121298.910.999.890.010.999.891.10224
89.347.785.855.246.155.988.995.959.988.955.164.255.858.774.39847
120244.902.797.286.745.236.657.75124
59.977.380.118.872.630.050.043.134.005.003.627.881.108.377.99547
119190.000.109.989.109.989.000.01324
36.100.041.795.873.893.424.321.112.342.439.837.859.714.000.16347
118190.000.109.890.010.989.000.01324
36.100.041.758.216.251.634.520.102.543.615.261.285.714.000.16347
117Prime!    190.000.010.998.900.109.999.98724
36.100.004.179.582.162.775.798.689.757.726.128.597.140.000.16347
116190.000.001.099.998.900.000.01324
36.100.000.417.999.583.210.002.520.001.238.599.971.400.000.16347
115190.000.000.109.989.000.000.01324
36.100.000.041.795.820.012.102.520.121.002.859.714.000.000.16347
114190.000.000.010.890.000.000.01324
36.100.000.004.138.200.000.123.532.100.000.283.140.000.000.16347
113190.000.000.001.099.999.999.98724
36.100.000.000.417.999.999.996.269.999.999.971.400.000.000.16347
112Prime!    190.000.000.000.000.000.000.01324
36.100.000.000.000.000.000.004.940.000.000.000.000.000.000.16347
11122.623.548.028.556.264.119.73923
511.824.925.400.392.024.842.646.248.420.293.004.529.428.11545
11019.000.010.989.010.989.000.01323
361.000.417.582.538.340.363.010.363.043.835.285.714.000.16345
10919.000.000.109.998.900.000.01323
361.000.004.179.958.212.100.252.001.212.859.971.400.000.16345
10819.000.000.010.989.000.000.01323
361.000.000.417.582.000.121.252.121.000.285.714.000.000.16345
10719.000.000.000.000.000.000.01323
361.000.000.000.000.000.000.494.000.000.000.000.000.000.16345
10617.940.724.517.774.341.730.62323
Prime!    321.869.596.222.669.386.631.848.136.683.966.222.695.968.12345
1052.989.001.090.090.089.001.10222
8.934.127.516.559.740.344.989.894.430.479.556.157.214.39843
1042.357.467.953.558.184.415.58122
5.557.655.152.053.813.952.504.052.593.183.502.515.567.55543
1032.274.085.312.164.984.327.18922
5.171.464.007.004.514.214.368.634.124.154.007.004.641.71543
1021.971.299.786.607.701.700.08322
3.886.022.848.679.570.259.020.209.520.759.768.482.206.88343
1011.900.010.998.910.998.900.01322
3.610.041.795.982.771.863.211.123.681.772.895.971.400.16343
1001.900.001.099.890.010.999.98722
3.610.004.179.583.251.557.986.897.551.523.859.714.000.16343
991.900.001.089.001.089.000.01322
3.610.004.138.205.324.123.421.243.214.235.028.314.000.16343
98Prime!    1.900.000.109.999.890.000.01322
3.610.000.417.999.594.100.025.200.014.959.997.140.000.16343
971.900.000.010.998.900.000.01322
3.610.000.041.795.820.121.025.201.210.285.971.400.000.16343
961.900.000.001.089.000.000.01322
3.610.000.004.138.200.001.235.321.000.028.314.000.000.16343
951.900.000.000.109.999.999.98722
3.610.000.000.417.999.999.962.699.999.997.140.000.000.16343
94Prime!    1.900.000.000.000.000.000.01322
3.610.000.000.000.000.000.049.400.000.000.000.000.000.16343
93301.806.053.492.395.203.44521
91.086.893.924.654.514.978.187.941.545.642.939.868.01941
92223.254.770.272.607.566.93021
49.842.692.449.474.779.384.748.397.747.494.429.624.89441
91190.001.098.901.098.900.01321
36.100.417.583.625.165.630.103.656.152.638.571.400.16341
90190.000.010.999.890.000.01321
36.100.004.179.958.321.002.520.012.385.997.140.000.16341
89190.000.001.098.900.000.01321
36.100.000.417.582.001.212.521.210.028.571.400.000.16341
88190.000.000.000.000.000.01321
36.100.000.000.000.000.004.940.000.000.000.000.000.16341
87179.273.560.813.749.449.37321
32.139.009.606.841.122.136.463.122.114.860.690.093.12341
8629.887.863.462.313.219.39820
893.284.382.341.877.542.646.245.778.143.283.482.39839
8529.194.215.854.335.739.79220
852.302.239.349.548.269.232.962.845.943.932.203.25839
8422.136.594.424.165.328.51020
490.028.812.699.987.512.121.215.789.996.218.820.09439
8319.000.109.891.098.900.01320
361.004.175.873.834.254.111.452.438.378.571.400.16339
8219.000.010.989.010.999.98720
361.000.417.582.538.757.868.757.835.285.714.000.16339
8119.000.001.099.890.000.01320
361.000.041.795.821.210.252.012.128.597.140.000.16339
8019.000.000.108.900.000.01320
361.000.004.138.200.012.353.210.002.831.400.000.16339
7919.000.000.010.999.999.98720
361.000.000.417.999.999.626.999.999.714.000.000.16339
7819.000.000.000.000.000.01320
361.000.000.000.000.000.494.000.000.000.000.000.16339
772.312.329.819.296.526.77119
5.346.869.193.207.908.150.518.097.023.919.686.43537
761.921.415.725.491.503.06319
3.691.838.390.166.039.053.509.306.610.938.381.96337
751.906.832.280.402.026.28719
3.636.009.345.583.191.803.081.913.855.439.006.36337
741.900.010.890.108.900.01319
3.610.041.382.532.414.521.254.142.352.831.400.16337
731.900.001.099.989.000.01319
3.610.004.179.959.410.025.200.149.599.714.000.16337
721.900.000.109.890.000.01319
3.610.000.417.582.012.125.212.102.857.140.000.16337
71Prime!    1.900.000.000.000.000.01319
3.610.000.000.000.000.049.400.000.000.000.000.16337
70Prime!    1.733.210.971.745.809.74719
3.004.020.272.580.054.113.114.500.852.720.204.00337
69223.356.252.482.559.17018
49.888.015.523.052.719.391.725.032.551.088.89435
68190.010.989.109.890.01318
36.104.175.982.518.741.114.781.528.957.140.16335
67190.001.098.901.099.98718
36.100.417.583.625.578.687.552.638.571.400.16335
66190.000.109.989.000.01318
36.100.041.795.832.102.520.123.859.714.000.16335
65Prime!    190.000.010.890.000.01318
36.100.004.138.200.123.532.100.283.140.000.16335
64190.000.001.099.999.98718
36.100.000.417.999.996.269.999.971.400.000.16335
63190.000.000.000.000.01318
36.100.000.000.000.004.940.000.000.000.000.16335
6230.265.582.368.509.97517
916.005.476.105.061.868.160.501.674.500.61933
6123.029.141.616.879.67917
530.341.363.610.299.595.992.016.363.143.03533
6019.000.010.989.000.01317
361.000.417.582.121.252.121.285.714.000.16333
5919.000.000.000.000.01317
361.000.000.000.000.494.000.000.000.000.16333
581.900.108.910.890.01316
3.610.413.873.243.631.363.423.783.140.16331
571.900.010.998.900.01316
3.610.041.795.941.025.201.495.971.400.16331
561.900.010.891.099.98716
3.610.041.386.298.566.658.926.831.400.16331
551.900.001.089.000.01316
3.610.004.138.201.235.321.028.314.000.16331
541.900.000.109.999.98716
3.610.000.417.999.962.699.997.140.000.16331
53Prime!    1.900.000.000.000.01316
3.610.000.000.000.049.400.000.000.000.16331
52302.142.579.927.31515
91.290.138.605.133.933.150.683.109.21929
51296.255.835.953.97215
87.767.520.336.786.768.763.302.576.77829
50190.001.098.900.01315
36.100.417.583.212.521.238.571.400.16329
49190.000.000.000.01315
36.100.000.000.004.940.000.000.000.16329
4830.274.870.968.87514
916.567.812.182.030.281.218.765.61927
4730.166.868.936.75514
910.039.981.447.353.744.189.930.01927
4619.001.089.109.98714
361.041.387.365.666.563.783.140.16327
45Prime!    19.000.108.900.01314
361.004.138.212.353.212.831.400.16327
4419.000.010.999.98714
361.000.417.999.626.999.714.000.16327
4319.000.000.000.01314
361.000.000.000.494.000.000.000.16327
421.900.109.890.01313
3.610.417.594.125.214.957.140.16325
411.900.000.000.01313
3.610.000.000.049.400.000.000.16325
40227.544.887.93912
51.776.676.027.172.067.667.71523
39226.152.547.98912
51.144.974.961.916.947.944.11523
38221.502.874.81012
49.063.523.549.094.532.536.09423
37190.108.910.98712
36.141.398.036.663.089.314.16323
36190.010.890.01312
36.104.138.323.532.383.140.16323
35190.001.099.98712
36.100.417.996.269.971.400.16323
34190.000.000.01312
36.100.000.004.940.000.000.16323
33181.584.343.07712
32.972.873.650.705.637.827.92323
3230.181.812.65511
910.941.815.141.518.149.01921
3129.634.602.12211
878.209.642.929.246.902.87821
3024.452.608.65111
597.930.069.838.960.039.79521
2919.000.000.01311
361.000.000.494.000.000.16321
282.988.003.95210
8.928.167.617.167.618.29819
27Prime!    1.901.089.01310
3.614.139.435.349.314.16319
26Prime!    1.900.109.98710
Prime!    3.610.417.962.697.140.16319
251.900.000.01310
3.610.000.049.400.000.16319
24Prime!    191.098.9139
36.518.794.549.781.56317
23190.000.0139
36.100.004.940.000.16317
2229.848.3488
890.923.878.329.09815
2122.213.8808
493.456.464.654.39415
2019.010.9878
361.417.626.714.16315
19Prime!    19.000.0138
361.000.494.000.16315
182.930.6927
8.588.955.598.85813
172.316.1297
5.364.453.544.63513
162.220.5207
4.930.709.070.39413
15Prime!    1.900.7637
3.612.899.982.16313
141.900.0137
3.610.049.400.16313
13302.1356
91.285.558.21911
12191.0876
36.514.241.56311
11190.0136
Prime!    36.104.940.16311
1030.2755
916.575.6199
9Prime!    19.0135
361.494.1639
82.2614
5.112.1157
7Prime!    1.9134
3.659.5637
61.8574
3.448.4437
52923
85.2585
4Prime!    31
Prime!    31
3Prime!    21
–21
211
–51
101
–61
up down
[SD7] Case X = 7
One can find the regular numbers of the form n2 – 7 at
%N n2 – 7. under A028881.
The palindromic numbers of the form n2 – 7 are categorised as follows :
%N n2 – 7 is a palindrome. under A0?????.
%N Palindromes of the form n2 – 7. under A0?????.

More terms from Robert Xiao, Nov 11, 2022. See Index Nrs 97 up to 125.
More terms from Robert Xiao, Dec 6, 2022. See Index Nrs 126 up to 152.
More terms from Patrick De Geest, Jun 20, 2023. See Index Nrs 153 up to 159.
More terms from Patrick De Geest, Jul 9, 2023. See Index Nrs 160 up to 168.
1682.790.000.010.999.890.001.099.999.87828
7.784.100.061.379.386.327.135.579.355.539.755.317.236.839.731.600.014.87755
1672.790.000.010.989.001.098.900.000.12228
7.784.100.061.318.626.252.620.145.832.385.410.262.526.268.131.600.014.87755
1662.790.000.001.099.999.989.000.000.12228
7.784.100.006.137.999.939.830.000.656.560.000.389.399.997.316.000.014.87755
1652.790.000.001.099.890.010.999.999.87828
7.784.100.006.137.386.262.589.757.355.537.579.852.626.837.316.000.014.87755
1642.790.000.000.109.999.890.000.000.12228
7.784.100.000.613.799.386.212.100.656.560.012.126.839.973.160.000.014.87755
1632.790.000.000.010.998.900.000.000.12228
7.784.100.000.061.373.862.000.121.656.561.210.002.683.731.600.000.014.87755
1622.790.000.000.000.109.999.999.999.87828
7.784.100.000.000.613.799.999.999.331.339.999.999.973.160.000.000.014.87755
1612.000.000.000.000.000.000.000.000.00028
3.999.999.999.999.999.999.999.999.999.999.999.999.999.999.999.999.999.99354
1601.635.965.802.735.842.898.155.924.11328
2.676.384.107.721.130.838.596.786.195.916.876.958.380.311.277.014.836.76255
159279.000.010.998.901.099.890.000.12227
77.841.006.137.386.934.714.445.473.237.454.441.743.968.373.160.014.87753
158279.000.000.109.999.989.000.000.12227
77.841.000.061.379.993.874.100.065.656.000.147.839.997.316.000.014.87753
157279.000.000.010.999.890.000.000.12227
77.841.000.006.137.938.620.121.065.656.012.102.683.973.160.000.014.87753
156279.000.000.001.098.900.000.000.12227
77.841.000.000.613.186.200.001.275.657.210.000.268.131.600.000.014.87753
155218.322.779.368.034.433.407.897.54127
47.664.835.990.983.441.674.054.607.570.645.047.614.438.909.953.846.67453
154200.000.000.000.000.000.000.000.00027
39.999.999.999.999.999.999.999.999.999.999.999.999.999.999.999.999.99353
153148.737.378.440.853.162.548.579.62327
22.122.807.745.457.571.155.318.572.427.581.355.117.575.454.770.822.12253
15227.900.010.998.900.109.989.000.12226
778.410.613.738.747.113.189.836.323.638.981.311.747.837.316.014.87751
15127.900.001.099.989.000.109.999.87826
778.410.061.379.387.416.113.793.555.397.311.614.783.973.160.014.87751
15027.900.000.109.989.001.099.999.87826
778.410.006.137.386.273.477.573.555.375.774.372.683.731.600.014.87751
14927.900.000.010.999.989.000.000.12226
778.410.000.613.799.386.321.006.565.600.123.683.997.316.000.014.87751
14827.900.000.001.099.890.000.000.12226
778.410.000.061.373.862.001.216.565.612.100.268.373.160.000.014.87751
14727.900.000.000.010.999.999.999.87826
778.410.000.000.613.799.999.993.313.399.999.997.316.000.000.014.87751
14621.257.625.429.129.412.776.923.11926
451.886.638.885.169.450.716.133.545.331.617.054.961.588.836.688.15451
14520.000.000.000.000.000.000.000.00026
399.999.999.999.999.999.999.999.999.999.999.999.999.999.999.999.99351
1442.790.000.109.890.109.890.000.12225
7.784.100.613.186.825.262.036.932.396.302.625.286.813.160.014.87749
1432.790.000.010.999.998.900.000.12225
7.784.100.061.379.993.983.000.656.560.003.893.999.731.600.014.87749
1422.790.000.001.099.989.000.000.12225
7.784.100.006.137.938.621.210.656.560.121.268.397.316.000.014.87749
1412.790.000.000.109.890.000.000.12225
7.784.100.000.613.186.200.012.756.572.100.026.813.160.000.014.87749
1402.000.000.000.000.000.000.000.00025
3.999.999.999.999.999.999.999.999.999.999.999.999.999.999.999.99349
1391.999.898.765.463.975.546.318.60025
3.999.595.072.104.333.469.360.810.180.639.643.334.012.705.959.99349
138311.297.279.351.038.129.460.17624
96.905.996.131.358.270.175.632.823.657.107.285.313.169.950.96947
137279.000.010.998.900.109.999.87824
77.841.006.137.386.382.355.735.553.755.328.368.373.160.014.87747
136279.000.001.099.998.900.000.12224
77.841.000.613.799.387.410.065.656.001.478.399.731.600.014.87747
135279.000.000.109.989.000.000.12224
77.841.000.061.373.862.012.165.656.121.026.837.316.000.014.87747
134279.000.000.001.099.999.999.87824
77.841.000.000.613.799.999.933.133.999.999.731.600.000.014.87747
133200.000.000.000.000.000.000.00024
39.999.999.999.999.999.999.999.999.999.999.999.999.999.999.99347
132150.051.596.596.610.047.256.47724
22.515.481.641.191.795.916.883.138.861.959.719.114.618.451.52247
13127.900.000.109.998.900.000.12223
778.410.006.137.938.632.106.565.601.236.839.731.600.014.87745
13027.900.000.010.989.000.000.12223
778.410.000.613.186.200.127.565.721.002.681.316.000.014.87745
12927.110.582.738.794.060.475.53823
734.983.696.436.998.461.086.727.680.164.899.634.696.389.43745
12820.951.617.802.286.091.180.72123
438.970.288.533.071.457.354.060.453.754.170.335.882.079.83445
12720.000.000.000.000.000.000.00023
399.999.999.999.999.999.999.999.999.999.999.999.999.999.99345
12616.806.944.809.328.008.011.01723
282.473.393.823.797.671.557.252.755.176.797.328.393.374.28245
1252.790.001.099.890.010.999.87822
7.784.106.137.387.471.137.355.537.311.747.837.316.014.87743
1242.790.000.109.999.890.000.12222
7.784.100.613.799.398.300.656.560.038.939.973.160.014.87743
1232.790.000.109.890.109.999.87822
7.784.100.613.186.825.875.155.515.785.286.813.160.014.87743
1222.790.000.010.998.900.000.12222
7.784.100.061.373.862.121.656.561.212.683.731.600.014.87743
1212.790.000.000.109.999.999.87822
7.784.100.000.613.799.999.331.339.999.973.160.000.014.87743
1202.000.000.000.000.000.000.00022
3.999.999.999.999.999.999.999.999.999.999.999.999.999.99343
1191.636.089.565.484.996.964.11322
2.676.789.066.288.886.169.319.139.616.888.826.609.876.76243
1181.570.069.033.298.291.293.34322
2.465.116.769.322.230.934.071.704.390.322.239.676.115.64243
117279.000.010.999.890.000.12221
77.841.006.137.938.741.065.656.014.783.973.160.014.87741
116279.000.001.098.900.000.12221
77.841.000.613.186.201.275.657.210.268.131.600.014.87741
115208.440.890.107.114.759.22921
43.447.604.668.646.291.503.130.519.264.686.640.674.43441
114200.000.000.000.000.000.00021
39.999.999.999.999.999.999.999.999.999.999.999.999.99341
11330.056.473.917.808.171.35420
903.391.624.371.882.885.333.588.288.173.426.193.30939
11227.900.010.989.010.999.87820
778.410.613.186.934.551.555.155.439.681.316.014.87739
11127.900.001.099.890.000.12220
778.410.061.373.863.216.565.612.368.373.160.014.87739
11027.900.000.010.999.999.87820
778.410.000.613.799.993.313.399.997.316.000.014.87739
10927.492.388.608.700.057.74220
755.831.431.411.780.696.646.696.087.114.134.138.55739
10826.734.569.572.390.105.13220
714.737.210.220.966.848.767.848.669.022.012.737.41739
10720.000.000.000.000.000.00020
399.999.999.999.999.999.999.999.999.999.999.999.99339
10616.866.054.311.204.303.68319
284.463.788.028.493.278.747.872.394.820.887.364.48239
1053.035.644.269.098.351.05619
9.215.136.128.509.662.000.002.669.058.216.315.12937
1042.856.643.144.817.999.62519
8.160.410.056.835.670.777.770.765.386.500.140.61837
1032.849.941.814.197.331.58519
8.122.168.344.310.377.666.667.730.134.438.612.21837
1022.790.001.099.989.000.12219
7.784.106.137.939.830.656.560.389.397.316.014.87737
1012.790.000.109.890.000.12219
7.784.100.613.186.212.756.572.126.813.160.014.87737
1002.182.976.764.371.344.20919
4.765.387.553.785.183.255.523.815.873.557.835.67437
992.168.606.056.899.582.24119
4.702.852.230.021.554.128.214.551.200.322.582.07437
982.000.000.000.000.000.00019
3.999.999.999.999.999.999.999.999.999.999.999.99337
971.437.763.911.438.909.60319
2.067.165.065.036.112.695.962.116.305.605.617.60237
96314.309.382.828.649.28618
98.790.388.134.126.414.641.462.143.188.309.78935
95310.611.630.541.308.42618
Prime!    96.479.585.027.530.285.358.203.572.058.597.46935
94284.699.058.477.202.74518
81.053.553.897.805.708.180.750.879.835.535.01835
93279.000.109.989.000.12218
77.841.061.373.874.165.656.147.837.316.014.87735
92279.000.001.099.999.87818
77.841.000.613.799.933.133.999.731.600.014.87735
91213.060.011.257.408.23118
45.394.568.397.006.922.122.960.079.386.549.35435
90200.000.000.000.000.00018
39.999.999.999.999.999.999.999.999.999.999.99335
89199.976.057.913.842.10018
39.990.423.738.760.329.592.306.783.732.409.99335
88142.415.321.989.339.70318
20.282.123.937.327.304.740.372.373.932.128.20235
8727.900.010.989.000.12217
778.410.613.186.327.565.723.681.316.014.87733
8620.000.000.000.000.00017
399.999.999.999.999.999.999.999.999.999.99333
853.133.131.413.639.51416
9.816.512.455.134.739.374.315.542.156.18931
842.790.010.998.900.12216
7.784.161.373.983.656.563.893.731.614.87731
832.790.000.109.999.87816
7.784.100.613.799.331.339.973.160.014.87731
822.000.000.000.000.00016
3.999.999.999.999.999.999.999.999.999.99331
811.997.009.863.505.33016
3.988.048.394.937.576.757.394.938.408.89331
80307.703.972.678.78415
94.681.734.802.305.850.320.843.718.64929
79303.842.998.768.34415
92.320.567.900.539.893.500.976.502.32929
78279.001.098.900.12215
77.841.613.187.475.657.478.131.614.87729
77217.750.934.842.30915
47.415.469.624.699.499.642.696.451.47429
76208.939.304.470.62915
43.655.632.952.670.207.625.923.655.63429
75208.417.441.681.52115
43.437.829.997.070.207.079.992.873.43429
74200.000.000.000.00015
39.999.999.999.999.999.999.999.999.99329
7327.900.010.999.87814
778.410.613.793.313.397.316.014.87727
7222.217.531.211.79914
493.618.693.147.262.741.396.816.39427
7120.000.000.000.00014
399.999.999.999.999.999.999.999.99327
7015.689.702.164.40714
246.166.754.007.797.700.457.661.64227
693.010.534.949.20413
9.063.320.680.378.730.860.233.60925
682.847.385.777.70513
8.107.605.767.076.707.675.067.01825
672.790.109.890.12213
7.784.713.198.956.598.913.174.87725
662.000.000.000.00013
3.999.999.999.999.999.999.999.99325
651.674.399.042.96713
2.803.612.155.088.805.512.163.08225
641.640.692.403.06313
2.691.871.561.468.641.651.781.96225
631.438.749.187.14713
2.069.999.223.516.153.229.999.60225
621.416.714.309.24713
2.007.079.434.025.204.349.707.00225
61285.129.510.43512
81.298.837.720.902.773.889.21823
60279.001.099.87812
77.841.613.733.133.731.614.87723
59200.000.000.00012
39.999.999.999.999.999.999.99323
58198.455.185.22012
39.384.460.540.704.506.448.39323
57197.644.202.69012
39.063.230.856.965.803.236.09323
56169.804.109.16712
28.833.435.489.998.453.433.88223
5531.372.742.13611
984.248.949.131.949.842.48921
5420.000.000.00011
399.999.999.999.999.999.99321
5316.870.518.06711
284.614.379.848.973.416.48221
5214.895.699.37711
221.881.859.929.958.188.12221
512.790.109.87810
7.784.713.131.313.174.87719
50Prime!    2.088.111.87110
4.360.211.185.811.120.63419
492.048.625.66110
4.196.867.098.907.686.91419
482.000.000.00010
3.999.999.999.999.999.99319
471.508.870.97310
2.276.691.613.161.966.72219
461.417.005.75310
2.007.905.304.035.097.00219
45271.226.1129
Prime!    73.563.603.830.636.53717
44222.706.4499
49.598.162.426.189.59417
43200.000.0009
39.999.999.999.999.99317
42163.636.3639
26.776.859.295.867.76217
41161.682.7639
26.141.315.851.314.16217
40148.953.1279
22.187.034.043.078.12217
3928.495.9858
812.021.161.120.21815
3827.791.2228
772.352.020.253.27715
3720.000.0008
399.999.999.999.99315
362.850.1157
8.123.155.513.21813
352.787.9727
7.772.787.872.77713
342.780.2227
7.729.634.369.27713
332.143.7817
4.595.796.975.95413
322.000.0007
3.999.999.999.99313
311.996.6307
3.986.531.356.89313
30Prime!    1.636.3637
2.677.683.867.76213
291.569.8437
2.464.407.044.64213
28Prime!    212.9816
45.360.906.35411
27200.0006
39.999.999.99311
2627.1125
735.060.5379
2526.6825
Prime!    711.929.1179
2420.0005
399.999.9939
23Prime!    16.3635
267.747.7629
2215.5575
242.020.2429
212.0794
4.322.2347
20Prime!    2.0394
4.157.5147
192.0004
3.999.9937
18Prime!    1.6374
2.679.7627
171.5574
2.424.2427
163143
98.5895
152853
81.2185
142783
77.2775
132683
71.8175
122003
39.9935
11Prime!    1633
26.5625
10Prime!    1573
24.6425
9282
7773
8212
4343
7202
3933
6Prime!    172
2823
541
91
4Prime!    31
Prime!    21
3Prime!    21
–31
211
–61
101
–71
up down
[SD8] Case X = 8
One can find the regular numbers of the form n2 – 8 at
%N n2 – 8. under A028884.
The palindromic numbers of the form n2 – 8 are categorised as follows :
%N n2 – 8 is a palindrome. under A0?????.
%N Palindromes of the form n2 – 8. under A0?????.

More terms from Robert Xiao, Nov 11, 2022. See Index Nrs 86 up to 103.
More terms from Robert Xiao, Dec 6, 2022. See Index Nrs 104 up to 125.
More terms from Patrick De Geest, Jun 20, 2023. See Index Nrs 126 up to 131.
More terms from Patrick De Geest, Jul 9, 2023. See Index Nrs 132 up to 139.
1392.908.648.926.564.036.734.407.819.71628
8.460.238.578.002.123.159.837.841.563.651.487.389.513.212.008.758.320.64855
138Prime!    1.999.999.999.999.999.999.999.999.99928
3.999.999.999.999.999.999.999.999.995.999.999.999.999.999.999.999.999.99355
1371.989.553.168.501.645.018.040.374.30128
3.958.321.810.294.935.093.958.935.409.045.398.593.905.394.920.181.238.59355
1361.711.812.442.494.739.935.700.019.52028
2.930.301.838.279.807.319.215.914.391.934.195.129.137.089.728.381.030.39255
1351.374.157.005.636.112.318.551.547.91728
1.888.307.476.138.806.422.413.440.929.290.443.142.246.088.316.747.038.88155
1341.293.001.594.152.504.107.393.268.38728
1.671.853.122.480.916.943.925.343.921.293.435.293.496.190.842.213.581.76155
1331.270.954.030.950.611.959.715.077.48728
1.615.324.148.789.609.103.235.813.865.683.185.323.019.069.878.414.235.16155
1321.000.000.000.000.000.000.000.000.00328
1.000.000.000.000.000.000.000.000.006.000.000.000.000.000.000.000.000.00155
131266.861.848.309.507.705.639.818.71527
71.215.246.083.166.700.690.359.109.190.195.309.600.766.138.064.251.21753
130Prime!    199.999.999.999.999.999.999.999.99927
39.999.999.999.999.999.999.999.999.599.999.999.999.999.999.999.999.99353
129189.605.423.993.949.309.436.941.21927
35.950.216.807.925.288.500.633.493.039.433.600.588.252.970.861.205.95353
128170.529.677.035.804.450.194.172.59027
29.080.370.749.935.771.654.831.636.763.613.845.617.753.994.707.308.09253
127104.145.009.154.145.635.273.577.05327
10.846.182.931.717.078.169.515.676.167.651.596.187.071.713.928.164.80153
126100.000.000.000.000.000.000.000.00327
10.000.000.000.000.000.000.000.000.600.000.000.000.000.000.000.000.00153
12526.442.365.753.077.695.030.276.99826
699.198.706.619.536.137.824.555.616.555.428.731.635.916.607.891.99651
12426.372.340.503.646.043.417.051.09826
695.500.343.640.249.646.957.803.757.308.759.646.942.046.343.005.59651
12319.999.999.999.999.999.999.999.99926
Prime!    399.999.999.999.999.999.999.999.959.999.999.999.999.999.999.999.99351
12217.809.796.586.604.857.111.000.93926
317.188.854.456.242.019.617.410.545.014.716.910.242.654.458.881.71351
12112.852.940.042.477.312.975.833.91326
165.198.067.735.516.711.883.551.585.155.388.117.615.537.760.891.56151
12010.424.035.513.550.143.872.444.05326
108.660.516.387.754.611.696.534.959.435.696.116.457.783.615.066.80151
11910.000.000.000.000.000.000.000.00326
100.000.000.000.000.000.000.000.060.000.000.000.000.000.000.000.00151
1182.969.300.680.912.598.840.579.51425
8.816.746.533.668.023.116.632.761.672.366.113.208.663.356.476.18849
1171.999.999.999.999.999.999.999.99925
3.999.999.999.999.999.999.999.995.999.999.999.999.999.999.999.99349
116Prime!    1.978.665.475.782.894.231.896.35125
3.915.117.065.055.147.200.072.830.382.700.027.415.505.607.115.19349
1151.720.298.876.035.320.843.628.64025
2.959.428.222.888.388.191.188.689.868.811.918.838.882.228.249.59249
1141.718.592.262.911.847.638.472.44025
2.953.559.366.140.465.236.034.883.884.306.325.640.416.639.553.59249
1131.284.972.343.422.809.343.672.66325
1.651.153.923.361.506.275.141.475.741.415.726.051.633.293.511.56149
1121.000.000.000.000.000.000.000.00325
Prime!    1.000.000.000.000.000.000.000.006.000.000.000.000.000.000.000.00149
111199.999.999.999.999.999.999.99924
39.999.999.999.999.999.999.999.599.999.999.999.999.999.999.99347
110178.305.303.670.979.298.116.93924
31.792.781.317.200.143.565.149.494.156.534.100.271.318.729.71347
109112.698.731.544.844.262.684.97324
12.701.004.091.816.875.291.309.490.319.257.861.819.040.010.72147
108100.000.000.000.000.000.000.00324
10.000.000.000.000.000.000.000.600.000.000.000.000.000.000.00147
10726.394.809.691.525.815.996.05223
696.685.978.651.865.141.777.828.777.141.568.156.879.586.69645
10626.304.615.186.261.243.512.69823
691.932.780.097.285.634.738.787.837.436.582.790.087.239.19645
10519.999.999.999.999.999.999.99923
3.999.99.999.999.999.999.999.959.999.999.999.999.999.999.99345
10410.000.000.000.000.000.000.00323
100.000.000.000.000.000.000.060.000.000.000.000.000.000.00145
1032.566.328.708.401.359.382.30822
6.586.043.039.564.989.474.245.424.749.894.659.303.406.85643
1021.999.999.999.999.999.999.99922
3.999.999.999.999.999.999.995.999.999.999.999.999.999.99343
1011.816.878.193.472.801.461.92922
3.301.046.369.916.990.580.818.180.850.996.199.636.401.03343
1001.000.000.000.000.000.000.00322
1.000.000.000.000.000.000.006.000.000.000.000.000.000.00143
99293.635.854.920.506.795.82621
86.222.015.294.896.915.057.675.051.969.849.251.022.26841
98266.890.263.033.363.793.11521
71.230.412.502.018.112.039.393.021.181.020.521.403.21741
97199.999.999.999.999.999.99921
39.999.999.999.999.999.999.599.999.999.999.999.999.99341
96127.974.948.145.989.224.03721
16.377.587.352.968.630.730.703.703.686.925.378.577.36141
95127.107.421.661.491.546.26321
16.156.296.641.432.210.355.155.301.223.414.669.265.16141
94100.000.000.000.000.000.00321
10.000.000.000.000.000.000.600.000.000.000.000.000.00141
9319.999.999.999.999.999.99920
399.999.999.999.999.999.959.999.999.999.999.999.99339
9217.042.910.334.886.818.79020
290.460.792.682.991.937.797.739.199.286.297.064.09239
9110.000.000.000.000.000.00320
100.000.000.000.000.000.060.000.000.000.000.000.00139
901.999.999.999.999.999.99919
3.999.999.999.999.999.995.999.999.999.999.999.99337
891.817.680.096.036.395.32119
3.303.960.931.526.879.317.139.786.251.390.693.03337
881.726.463.835.915.258.53019
2.980.677.376.723.228.729.278.223.276.737.760.89237
871.002.276.416.671.259.00319
1.004.558.015.415.379.191.919.735.145.108.554.00137
86Prime!    1.000.000.000.000.000.00319
1.000.000.000.000.000.006.000.000.000.000.000.00137
85255.601.656.911.517.44218
65.332.207.015.913.072.127.031.951.070.223.35635
84252.907.003.473.721.78818
63.961.952.406.057.124.542.175.060.425.916.93635
83199.999.999.999.999.99918
39.999.999.999.999.999.599.999.999.999.999.99335
82194.078.902.903.092.45918
37.666.620.552.067.990.509.976.025.502.666.67335
81183.337.479.874.002.37118
33.612.631.526.550.224.442.205.562.513.621.63335
80Prime!    100.000.000.000.000.00318
10.000.000.000.000.000.600.000.000.000.000.00135
7926.759.770.846.386.82517
716.085.335.751.134.252.431.157.533.580.61733
7819.999.999.999.999.99917
Prime!    399.999.999.999.999.959.999.999.999.999.99333
7710.313.548.756.006.85317
106.369.287.942.530.505.035.249.782.963.60133
7610.000.000.000.000.00317
100.000.000.000.000.060.000.000.000.000.00133
752.906.185.815.788.61616
8.445.915.995.890.943.490.985.995.195.44831
742.833.975.511.360.14616
8.031.417.198.989.001.009.898.917.141.30831
732.670.163.556.442.56516
7.129.773.418.154.007.004.518.143.779.21731
722.627.100.268.765.34816
6.901.655.822.146.963.696.412.285.561.09631
711.999.999.999.999.99916
3.999.999.999.999.995.999.999.999.999.99331
701.295.684.114.459.86316
1.678.797.324.463.639.363.644.237.978.76131
691.101.703.259.329.37316
1.213.750.071.616.963.696.161.700.573.12131
681.000.000.000.000.00316
1.000.000.000.000.006.000.000.000.000.00131
67199.999.999.999.99915
39.999.999.999.999.599.999.999.999.99329
66193.511.242.945.80915
37.446.601.146.431.913.464.110.664.47329
65181.886.803.762.17915
33.082.809.382.821.412.828.390.828.03329
64170.530.193.287.41015
29.080.546.822.641.414.622.864.508.09229
63130.122.803.816.31315
16.931.944.073.018.681.037.044.913.96129
62129.566.082.859.86315
16.787.369.827.648.884.672.896.378.76129
61100.000.000.000.00315
10.000.000.000.000.600.000.000.000.00129
6025.646.720.121.54214
657.754.252.992.707.299.252.457.75627
5919.999.999.999.99914
399.999.999.999.959.999.999.999.99327
5819.795.435.332.14914
391.859.259.989.292.989.952.958.19327
5718.339.849.698.37114
336.350.086.958.838.859.680.053.63327
5610.000.000.000.00314
100.000.000.000.060.000.000.000.00127
552.831.774.899.45413
8.018.949.081.177.711.809.498.10825
542.676.770.480.12513
7.165.100.203.268.623.020.015.61725
532.675.894.320.37513
7.160.410.413.815.183.140.140.61725
521.999.999.999.99913
3.999.999.999.995.999.999.999.99325
511.839.867.157.47113
Prime!    3.385.111.157.140.417.511.115.83325
501.010.273.888.29713
1.020.653.329.374.739.233.560.20125
491.000.000.000.00313
1.000.000.000.006.000.000.000.00125
48293.795.842.87612
86.315.997.291.219.279.951.36823
47266.623.495.19512
71.088.088.189.998.188.088.01723
46199.999.999.99912
39.999.999.999.599.999.999.99323
45173.192.892.40012
29.995.777.977.877.977.759.99223
44Prime!    100.000.000.00312
10.000.000.000.600.000.000.00123
4319.999.999.99911
399.999.999.959.999.999.99321
4219.295.962.59111
372.334.172.313.271.433.27321
4110.000.000.00311
100.000.000.060.000.000.00121
401.999.999.99910
3.999.999.995.999.999.99319
391.000.000.00310
1.000.000.006.000.000.00119
38286.740.1069
82.219.888.388.891.22817
37264.570.0029
69.997.285.958.279.99617
36199.999.9999
39.999.999.599.999.99317
35173.201.7009
29.998.828.882.889.99217
34127.813.0379
16.336.172.427.163.36117
33100.000.0039
10.000.000.600.000.00117
3229.731.0868
883.937.474.739.38815
31Prime!    19.999.9998
Prime!    399.999.959.999.99315
3010.000.0038
100.000.060.000.00115
292.871.2947
8.244.329.234.42813
281.999.9997
3.999.995.999.99313
27Prime!    1.211.5937
1.467.957.597.64113
261.184.2577
1.402.464.642.04113
251.121.9777
1.258.832.388.52113
24Prime!    1.000.0037
1.000.006.000.00113
23286.5566
82.114.341.12811
22Prime!    199.9996
39.999.599.99311
21120.8436
Prime!    14.603.030.64111
20Prime!    100.0036
10.000.600.00111
1928.3545
803.949.3089
1819.9995
399.959.9939
17Prime!    19.2595
370.909.0739
1617.2705
298.252.8929
1510.0035
Prime!    100.060.0019
142.5124
6.310.1367
13Prime!    1.9994
3.995.9937
12Prime!    1.3674
1.868.6817
11Prime!    1.1934
1.423.2417
101.0034
1.006.0017
9Prime!    1993
39.5935
8Prime!    1033
Prime!    10.6015
7Prime!    192
Prime!    3533
6Prime!    132
1613
541
81
4Prime!    31
11
3Prime!    21
–41
211
–71
101
–81
up down
[SD9] [QP6] Case X = 9
See in-depth webpage about Palindromic Quasipronic Numbers of the form n(n+6)
One can find the regular numbers of the form n2 – 9 at
%N n2 – 9 or n(n+6). under A028560.
The palindromic numbers of the form n2 – 9 are categorised as follows :
%N n2 – 9 or n(n+6) is a palindrome. under A028561.
%N Palindromes of the form n2 – 9 or n(n+6). under A028562.
3Prime!    22
–53
212
–83
101
–91


Contributions

[ November 11, 2022 ]
Robert Xiao (email) added
for Case X = 2 [n^2 - 2] entries [57] up to [64].
for Case X = 3 [n^2 - 3] entries [115] up to [145].
for Case X = 5 [n^2 - 5] entries [71] up to [89].
for Case X = 6 [n^2 - 6] entries [70] up to [105].
for Case X = 7 [n^2 - 7] entries [97] up to [125].
for Case X = 8 [n^2 - 8] entries [86] up to [103].

[ December 6, 2022 ]
Robert Xiao (email) added
for Case X = 2 [n^2 - 2] entries [65] up to [78].
for Case X = 3 [n^2 - 3] entries [146] up to [171].
for Case X = 5 [n^2 - 5] entries [90] up to [105].
for Case X = 6 [n^2 - 6] entries [106] up to [144].
for Case X = 7 [n^2 - 7] entries [126] up to [152].
for Case X = 8 [n^2 - 8] entries [104] up to [125].

[ June 20, 2023 ]
Robert Xiao (email) added
for Case X = 2 [n^2 - 2] entries [79] up to [83].
for Case X = 3 [n^2 - 3] entries [172] up to [175].
for Case X = 5 [n^2 - 5] entries [106] up to [111].
for Case X = 6 [n^2 - 6] entries [145] up to [155].
for Case X = 7 [n^2 - 7] entries [153] up to [159].
for Case X = 8 [n^2 - 8] entries [126] up to [131].

[ June 10, 2023 ]
Patrick De Geest (email) added
for Case X = 2 [n^2 - 2] entries [84] up to [87].
for Case X = 3 [n^2 - 3] entries [176] up to [182].
for Case X = 5 [n^2 - 5] entries [112] up to [115].
for Case X = 6 [n^2 - 6] entries [156] up to [174].
for Case X = 7 [n^2 - 7] entries [160] up to [168].
for Case X = 8 [n^2 - 8] entries [132] up to [139].
 

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Patrick De Geest - Belgium flag - Short Bio - Some Pictures
E-mail address : pdg@worldofnumbers.com