HOME plateWON | World!OfNumbers Palindromic Incremented Squaresof the form n^2+x n(n+0) n(n+1) n(n+2) n(n+x) n^2+1 n^2–x n^2+(n+1) n^2+(n+x)

Introduction

Palindromic numbers are numbers which read the same from
left to right (forwards) as from the right to left (backwards)
Here are a few random examples : 7, 3113, 44611644

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

 base2 + X

Palindromic Incremented Squares

Incremented 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

Incremented Squares of the form x2 + 1 can only start or end with a 0, 1, 2, 5, 6 or 7.
Even length palindromes of this form are not possible as they are never divisible by 11.
Alas, my palindromes may not have leading 0's! So the zero option must not be investigated.
1 can only be followed by 0 : 10
2 can only be followed by an even number : 20, 22, 24, 26 or 28
5 can only be followed by an even number : 50, 52, 54, 56 or 58
6 can only be followed by 2 : 62
7 can only be followed by an odd number : 71, 73, 75, 77 or 79

Incremented Squares of the form x2 + 2 can only start or end with a 1, 2, 3, 6, 7 or 8.
1 can only be followed by an odd number : 11, 13, 15, 17 or 19
2 can only be followed by 0 : 20
3 can only be followed by an even number : 30, 32, 34, 36 or 38
6 can only be followed by an even number : 60, 62, 64, 66 or 68
7 can only be followed by 2 : 72
8 can only be followed by an odd number : 81, 83, 85, 87 or 89
There are no palindromic quasipronics of type x^2 + 2 of lengths 10, 22, 24.

Incremented Squares of the form x2 + 3 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 odd number : 21, 23, 25, 27 or 29
3 can only be followed by 0 : 30
4 can only be followed by an even number : 40, 42, 44, 46 or 48
7 can only be followed by an even number : 70, 72, 74, 76 or 78
8 can only be followed by 2 : 82
9 can only be followed by an odd number : 91, 93, 95, 97 or 99
There are no palindromic quasipronics of type x^2 + 3 of EVEN lengths.

Incremented Squares of the form x2 + 4 can only start or end with a 0, 3, 4, 5, 8 or 9.
Even length palindromes of this form are not possible as they are never divisible by 11.
Alas, my palindromes may not have leading 0's! So the zero option must not be investigated.
3 can only be followed by an odd number : 31, 33, 35, 37 or 39
4 can only be followed by 0 : 40
5 can only be followed by an even number : 50, 52, 54, 56 or 58
8 can only be followed by an even number : 80, 82, 84, 86 or 88 { This 84... produces ever expanding Mandelbrot-like infinite palindromes }
9 can only be followed by 2 : 92
There are no palindromic quasipronics of type x^2 + 4 of EVEN lengths.

Incremented Squares of the form x2 + 5 can only start or end with a 0, 1, 4, 5, 6 or 9.
Even length palindromes of this form are not possible as they are never divisible by 11.
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 odd number : 41, 43, 45, 47 or 49
5 can only be followed by 0 : 50
6 can only be followed by an even number : 60, 60, 64, 66 or 68
9 can only be followed by an even number : 90, 92, 94, 96 or 98
There are no palindromic quasipronics of type x^2 + 5 of EVEN lengths nor of length 3.

Incremented Squares of the form x2 + 6 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 3 : 13
2 can only be followed by an even number : 20, 22, 24, 26 or 28
5 can only be followed by an odd number : 51, 53, 55, 57 or 59
6 can only be followed by 0 : 60
7 can only be followed by an even number : 70, 72, 74, 76 or 78
There are no palindromic quasipronics of type x^2 + 6 of lengths 6, 8, 12, 13, 26, 28, 32, 34, 42, 52, 54.

Incremented Squares of the form x2 + 7 can only start or end with a 1, 2, 3, 6, 7 or 8.
1 can only be followed by an odd number : 11, 13, 15, 17 or 19
2 can only be followed by 3 : 23
3 can only be followed by an even number : 30, 32, 34, 36 or 38
6 can only be followed by an odd number : 61, 63, 65, 67 or 69
7 can only be followed by 0 : 70
8 can only be followed by an even number : 80, 82, 84, 86 or 88
There are no palindromic quasipronics of type x^2 + 7 of lengths 7, 10, 18, 22, 28, 33, 37, 54.

Incremented Squares of the form x2 + 8 can only start or end with a 2, 3, 4, 7, 8 or 9.
2 can only be followed by an odd number : 21, 23, 25, 27 or 29
3 can only be followed by 3 : 33
4 can only be followed by an even number : 40, 42, 44, 46 or 48
7 can only be followed by an odd number : 71, 73, 75, 77 or 79
8 can only be followed by 0 : 80
9 can only be followed by an even number : 90, 92, 94, 96 or 98
There are no palindromic quasipronics of type x^2 + 8 of lengths 4, 14, 16, 24, 34, 38, 44, 46.

Incremented Squares of the form x2 + 9 can only start or end with a 0, 3, 4, 5, 8 or 9.
Even length palindromes of this form are not possible as they are never divisible by 11.
Alas, my palindromes may not have leading 0's! So the zero option must not be investigated.
3 can only be followed by an odd number : 31, 33, 35, 37 or 39
4 can only be followed by 3 : 43
5 can only be followed by an even number : 50, 52, 54, 56 or 58
8 can only be followed by an odd number : 81, 83, 85, 87 or 89
9 can only be followed by 0 : 90
There are no palindromic quasipronics of type x^2 + 9 of EVEN lengths.

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

An infinite palindromic pattern hides in the list for case n^2 + 3

212 + 3 = 444
2012 + 3 = 40404
20012 + 3 = 4004004
200012 + 3 = 400040004
2000012 + 3 = 40000400004
20000012 + 3 = 4000004000004
200000012 + 3 = 400000040000004

Two infinite palindromic pattern hide in the list for case n^2 + 4

202 + 4 = 404
2002 + 4 = 40004
20002 + 4 = 4000004
200002 + 4 = 400000004
2000002 + 4 = 40000000004
20000002 + 4 = 4000000000004
200000002 + 4 = 400000000000004
29122 + 4 = 8479748
290122 + 4 = 841696148
2900122 + 4 = 84106960148
29000122 + 4 = 8410069600148
290000122 + 4 = 841000696000148
2900000122 + 4 = 84100006960000148
29000000122 + 4 = 8410000069600000148

A finite palindromic pattern resides in the list for case n^2 + 5

(SQ5) 30990992 [960441585144069] {L=15}
(SQ5) 30990990992 [960441522666225144069] {L=21}
(SQ5) 30990990990992 [960441522603747306225144069] {L=27}
(SQ5) 30990990990990992 [is no longer palindromic] {L=33}

An infinite palindromic pattern hides in the list for case n^2 + 8

312 + 8 = 969
3012 + 8 = 90609
30012 + 8 = 9006009
300012 + 8 = 900060009
3000012 + 8 = 90000600009
30000012 + 8 = 9000006000009
300000012 + 8 = 900000060000009

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

302 + 9 = 909
3002 + 9 = 90009
30002 + 9 = 9000009
300002 + 9 = 900000009
3000002 + 9 = 90000000009
30000002 + 9 = 9000000000009
300000002 + 9 = 900000000000009

The Table

Index NrBasenumberLength
Palindromic Incremented Squares of form n^2+XLength

[PG4] Case X = 0  [Scanned exhaustively up to length 64]
See in-depth webpage about Palindromic Square Numbers

[SQ1] Case X = 1  [Scanned exhaustively up to length 55]
See in-depth webpage about Palindromic Incremented Squares

[SQ2] Case X = 2
One can find the regular numbers of the form n2 + 2 at
%N n^2 + 2. under A059100.
The palindromic numbers of the form n2 + 2 are categorised as follows :
%N n^2 + 2 is a palindrome. under A358207.
%N Palindromes of the form n^2 + 2. under A358237.

More terms from Robert Xiao, Nov 11, 2022. See Index Nrs 91 up to 111.
More terms from Robert Xiao, Dec 6, 2022. See Index Nrs 112 up to 127.
More terms from Patrick De Geest, Jun 19, 2023. See Index Nrs 128 up to 129.
More terms from Patrick De Geest, Jul 14, 2023. See Index Nrs 130 up to 132.
1321.428.316.028.006.361.066.718.545.02028
2.040.086.675.859.868.011.098.590.896.980.958.901.108.689.585.766.800.40254
131916.389.340.352.662.813.289.144.54427
839.769.423.111.988.485.549.535.855.558.535.945.584.889.111.324.967.93854
130602.577.719.619.508.869.099.605.01927
363.099.908.181.847.443.868.410.391.193.014.868.344.748.181.809.990.36354
129123.591.610.684.440.396.856.553.94327
15.274.886.231.574.281.661.539.538.583.593.516.618.247.513.268.847.25153
128105.891.703.736.116.146.190.821.45327
11.213.052.920.137.394.193.753.073.937.035.739.149.373.102.925.031.21153
12744.901.510.366.996.088.032.198.81026
2.016.145.633.237.457.168.163.439.009.343.618.617.547.323.365.416.10252
12629.872.883.496.454.789.838.468.53626
892.389.168.392.760.949.735.677.303.776.537.949.067.293.861.983.29851
12526.169.954.418.551.613.206.259.52226
684.866.514.269.069.103.652.661.323.166.256.301.960.962.415.668.48651
12412.248.802.545.629.742.628.376.25726
150.033.163.801.825.663.243.696.747.696.342.366.528.108.361.330.05151
1238.032.572.059.867.374.048.772.38825
64.522.213.896.961.988.579.493.911.939.497.588.916.969.831.222.54650
1221.854.745.513.059.461.147.400.02125
3.440.080.918.214.203.761.679.576.759.761.673.024.128.190.800.44349
1211.446.686.396.018.067.381.575.77025
2.092.901.528.423.744.486.274.341.434.726.844.473.248.251.092.90249
1201.400.710.615.968.555.905.639.13325
1.961.990.229.687.011.302.437.444.447.342.031.107.869.220.991.69149
119803.095.475.168.034.011.355.53824
644.962.342.235.370.333.359.697.796.953.333.073.532.243.269.44648
118416.169.018.182.025.072.028.78724
173.196.651.694.590.714.988.332.233.889.417.095.496.156.691.37148
117368.187.615.289.890.473.152.52324
135.562.120.052.856.388.926.534.435.629.883.658.250.021.265.53148
116296.368.975.679.479.443.673.37424
87.834.569.745.303.877.971.788.488.717.977.830.354.796.543.87847
11591.325.538.890.034.116.574.20623
8.340.354.053.555.133.861.148.888.411.683.315.553.504.530.43846
114Prime!    37.362.365.100.101.801.721.17323
1.395.946.325.873.305.116.148.558.416.115.033.785.236.495.93146
11326.875.237.747.365.350.628.33523
722.278.403.977.411.406.004.171.400.604.114.779.304.872.22745
112Prime!    18.088.246.998.535.700.200.93923
327.184.679.480.035.767.107.212.701.767.530.084.976.481.72345
1118.501.107.207.333.384.211.78522
72.268.823.750.575.610.700.122.100.701.657.505.732.886.22744
1104.517.711.868.396.279.486.48022
20.409.720.525.848.602.502.388.320.520.684.852.502.790.40244
1094.490.991.130.203.650.500.31022
20.169.001.331.567.862.081.066.018.026.876.513.310.096.10244
1082.688.724.003.510.559.421.31522
7.229.236.767.053.850.751.355.531.570.583.507.676.329.22743
1072.587.777.378.629.738.427.15822
6.696.591.761.347.800.596.110.116.950.087.431.671.956.96643
1061.393.832.487.516.711.897.93322
1.942.769.003.257.024.828.783.878.284.207.523.009.672.49143
1051.146.126.075.042.684.394.37322
1.313.604.979.892.749.019.774.779.109.472.989.794.063.13143
104606.280.044.424.636.623.31921
367.575.492.267.539.357.520.025.753.935.762.294.575.76342
103602.753.367.878.075.161.48121
363.311.622.488.362.209.894.498.902.263.884.226.113.36342
102438.438.630.529.582.551.76721
192.228.432.740.655.797.217.712.797.556.047.234.822.29142
101130.926.125.742.381.360.98721
17.141.650.401.909.855.283.638.255.890.910.405.614.17141
10081.399.838.754.317.152.79220
6.625.933.749.228.832.644.774.462.388.229.473.395.26640
9977.537.031.924.410.092.15220
6.011.991.319.646.989.798.338.979.896.469.131.991.10640
9829.239.637.086.105.459.38420
854.956.376.927.153.759.626.957.351.729.673.659.45839
9726.886.558.484.753.632.38520
722.887.027.154.077.540.646.045.770.451.720.788.22739
9626.884.378.685.311.911.91520
722.769.817.295.253.445.303.544.352.592.718.967.22739
9518.495.041.372.703.713.07920
342.066.555.378.022.047.404.740.220.873.555.660.24339
9414.384.850.021.015.389.64020
206.923.910.127.106.455.767.554.601.721.019.329.60239
939.439.517.858.975.957.48619
89.104.497.409.926.044.400.444.062.990.479.440.19838
921.956.888.260.602.318.15919
3.829.411.664.483.166.268.626.613.844.661.149.28337
911.799.563.347.308.938.11119
3.238.428.240.977.749.811.189.477.790.428.248.32337
90815.731.447.843.771.74218
665.417.795.001.296.097.790.692.100.597.714.56636
89570.673.738.705.892.53918
325.668.516.048.561.312.213.165.840.615.866.52336
88555.231.465.460.388.59918
308.281.980.237.290.697.796.092.732.089.182.80336
87441.054.463.993.293.43318
194.529.040.208.411.373.373.114.802.040.925.49136
86292.076.758.112.830.56618
85.308.832.629.700.935.853.900.792.623.880.35835
85253.886.289.305.421.53818
64.458.247.897.276.202.820.267.279.874.285.44635
84250.562.271.637.470.58218
62.781.451.968.129.594.849.592.186.915.418.72635
83191.231.972.873.754.91918
36.569.667.449.188.537.173.588.194.476.696.56335
8285.000.416.618.604.76517
7.225.070.825.336.381.111.836.335.280.705.22734
8162.174.257.361.897.95917
3.865.638.278.503.522.552.253.058.728.365.68334
8029.281.657.627.282.73417
857.415.473.401.405.111.504.104.374.514.75833
7917.401.046.324.368.60117
302.796.413.182.821.999.128.281.314.697.20333
7814.325.552.760.917.15017
205.221.461.905.820.979.028.509.164.122.50233
7714.208.781.036.651.41017
201.889.458.547.504.717.405.745.854.988.10233
765.550.595.170.515.84916
30.809.106.746.953.866.835.964.760.190.80332
754.369.111.126.470.46716
19.089.132.035.448.033.084.453.023.198.09132
74Prime!    3.703.941.221.122.77716
13.719.180.569.532.488.423.596.508.191.73132
732.923.563.521.564.61616
8.547.223.664.623.298.923.264.663.227.45831
721.851.301.394.474.17116
3.427.316.853.182.010.102.813.586.137.24331
71817.683.802.207.30815
668.606.800.392.199.991.293.008.606.86630
70791.470.648.804.93215
626.425.787.919.700.007.919.787.524.62630
69364.768.101.292.42715
133.055.767.720.482.284.027.767.550.33130
68284.676.297.563.00415
81.040.594.394.179.997.149.349.504.01829
67186.797.158.329.47115
34.893.178.359.965.456.995.387.139.84329
66141.426.468.677.10015
20.001.446.042.474.747.424.064.410.00229
65Prime!    140.737.100.319.08315
19.806.931.406.223.632.260.413.960.89129
64133.805.135.860.43715
17.903.814.382.630.003.628.341.830.97129
6393.455.496.826.37614
8.733.929.887.064.774.607.889.293.37828
6255.349.225.724.44914
3.063.536.788.296.006.928.876.353.60328
6145.492.981.517.64014
2.069.611.367.364.334.637.631.169.60228
6014.363.881.876.06014
206.321.102.549.404.945.201.123.60227
5913.413.161.997.31314
179.912.914.766.161.667.419.219.97127
5810.902.121.823.94714
118.856.260.264.181.462.062.658.81127
579.114.951.055.99413
83.082.332.753.166.135.723.328.03826
562.925.054.461.66613
8.555.943.603.712.173.063.495.55825
552.688.021.576.51513
7.225.459.995.810.185.999.545.22725
541.954.611.231.09113
3.820.505.064.707.074.605.050.28325
531.861.509.029.37913
3.465.215.866.459.546.685.125.64325
52268.803.849.76512
72.255.509.648.484.690.555.22723
51250.793.696.73212
62.897.478.320.502.387.479.82623
50144.598.910.53012
20.908.844.926.462.944.880.90223
49142.019.320.31012
20.169.487.341.314.378.496.10223
48Prime!    11.645.196.02311
135.610.590.414.095.016.53121
478.487.412.69510
72.036.174.255.247.163.02720
468.486.324.85510
72.017.709.544.590.771.02720
453.881.830.25710
15.068.606.144.160.686.05120
442.496.801.51810
6.234.017.820.287.104.32619
431.950.914.24110
3.806.066.375.736.606.08319
421.912.253.83110
3.656.714.714.174.176.56319
411.340.374.43710
1.796.603.631.363.066.97119
40849.937.6359
722.393.983.389.393.22718
39813.448.3589
661.698.231.132.896.16618
38620.208.5599
384.658.656.656.856.48318
37452.357.9209
204.627.687.786.726.40218
36451.977.3209
204.283.497.794.382.40218
35246.553.4489
60.788.602.720.688.70617
34186.062.6299
34.619.301.910.391.64317
3379.094.2828
6.255.905.445.095.52616
3261.875.0918
3.828.526.886.258.28316
3128.559.2548
815.630.989.036.51815
3026.237.6228
688.412.808.214.88615
2925.809.8928
666.150.525.051.66615
2814.365.9408
206.380.232.083.60215
275.513.9517
30.403.655.630.40314
262.491.0327
6.205.240.425.02613
251.845.5717
3.406.132.316.04313
24Prime!    1.050.5037
1.103.556.553.01113
23902.6966
814.860.068.41812
22423.4376
179.298.892.97112
21298.4366
89.064.046.09811
20268.8656
72.288.388.22711
19140.8336
19.833.933.89111
1810.5035
110.313.0119
174.5404
20.611.6028
163.6274
13.155.1318
152.9864
8.916.1987
142.9164
8.503.0587
132.5384
6.441.4467
12Prime!    1.8114
3.279.7237
118283
685.5866
103932
154.4516
92582
66.5665
8852
7.2274
7Prime!    192
3633
6Prime!    132
1713
581
662
4Prime!    31
Prime!    112
3Prime!    21
61
211
Prime!    31
101
Prime!    21

[SQ3] Case X = 3
One can find the regular numbers of the form n2 + 3 at
%N n^2 + 3. under A117950.
The palindromic numbers of the form n2 + 3 are categorised as follows :
%N n^2 + 3 is a palindrome. under A0?????.
%N Palindromes of the form n^2 + 3. under A0?????.

More terms from Robert Xiao, Nov 11, 2022. See Index Nrs 66 up to 77.
More terms from Robert Xiao, Dec 6, 2022. See Index Nrs 78 up to 91.
More terms from Patrick De Geest, Jun 19, 2023. See Index Nrs 92 up to 94.
More terms from Patrick De Geest, Jul 14, 2023. See Index Nr 95.
952.000.000.000.000.000.000.000.000.00128
4.000.000.000.000.000.000.000.000.004.000.000.000.000.000.000.000.000.00455
94286.826.430.926.120.797.748.596.46527
82.269.401.477.816.745.191.663.655.155.636.619.154.761.877.410.496.22853
93200.000.000.000.000.000.000.000.00127
40.000.000.000.000.000.000.000.000.400.000.000.000.000.000.000.000.00453
92154.710.076.848.513.419.991.387.92327
23.935.207.878.472.928.107.750.113.731.105.770.182.927.487.870.253.93253
9122.048.367.204.458.532.482.084.95926
486.130.496.382.642.562.696.151.707.151.696.265.246.283.694.031.68451
9020.000.000.000.000.000.000.000.00126
400.000.000.000.000.000.000.000.040.000.000.000.000.000.000.000.00451
892.868.304.107.548.013.666.233.08525
8.227.168.453.376.807.148.397.288.827.938.417.086.733.548.617.22849
882.000.000.000.000.000.000.000.00125
4.000.000.000.000.000.000.000.004.000.000.000.000.000.000.000.00449
871.673.076.503.597.660.563.183.93725
2.799.184.986.890.572.699.422.781.872.249.962.750.986.894.819.97249
861.652.907.186.843.584.537.304.71325
2.732.102.168.319.172.484.130.525.250.314.842.719.138.612.012.37249
851.588.152.745.829.359.228.852.30725
2.522.229.144.085.333.297.473.585.853.747.923.335.804.419.222.25249
84275.731.132.129.184.899.167.00824
76.027.657.225.242.020.985.938.683.958.902.024.252.275.672.06747
83200.000.000.000.000.000.000.00124
40.000.000.000.000.000.000.000.400.000.000.000.000.000.000.00447
82158.341.481.197.678.361.555.50724
25072024667874730.099.781.618.799.003.747.876.642.027.05247
8131.504.300.770.215.581.667.03623
992.520.967.020.206.092.257.646.752.290.602.020.769.025.29945
8020.000.000.000.000.000.000.00123
400.000.000.000.000.000.000.040.000.000.000.000.000.000.00445
7917.590.417.583.480.539.773.07023
309.422.790.761.221.352.436.313.634.253.122.167.097.224.90345
7817.471.838.836.772.834.261.25023
305.265.152.338.163.506.215.595.512.605.361.833.251.562.50345
772.015.292.079.957.069.919.55122
4.061.402.167.537.693.097.756.577.903.967.357.612.041.60443
762.000.000.000.000.000.000.00122
4.000.000.000.000.000.000.004.000.000.000.000.000.000.00443
75286.495.469.646.146.279.29521
82.079.654.127.765.924.075.957.042.956.772.145.697.02841
74216.652.393.128.330.371.53121
46.938.259.448.232.613.190.009.131.623.284.495.283.96441
73200.000.000.000.000.000.00121
40.000.000.000.000.000.000.400.000.000.000.000.000.00441
7228.740.278.113.777.786.02520
826.003.586.057.294.414.111.414.492.750.685.300.62839
7120.000.000.000.000.000.00120
400.000.000.000.000.000.040.000.000.000.000.000.00439
703.032.246.937.428.231.55419
9.194.521.489.542.889.605.069.882.459.841.254.91937
692.167.819.130.948.770.78119
4.699.439.784.507.483.798.973.847.054.879.349.96437
682.000.000.000.000.000.00119
4.000.000.000.000.000.004.000.000.000.000.000.00437
671.728.954.048.595.015.58319
2.989.282.102.153.095.506.055.903.512.012.829.89237
661.653.027.054.676.171.53719
2.732.498.443.491.378.604.068.731.943.448.942.37237
65286.777.606.421.144.18518
82.241.395.544.640.678.487.604.644.559.314.22835
64265.887.849.560.347.59818
70.696.348.543.826.036.363.062.834.584.369.60735
63265.769.807.591.493.40218
70.633.590.627.219.423.932.491.272.609.533.60735
62200.000.000.000.000.00118
40.000.000.000.000.000.400.000.000.000.000.00435
61174.471.663.807.316.38018
30.440.361.471.693.232.423.239.617.416.304.40335
6030.194.108.938.222.95417
911.684.214.573.275.282.572.375.412.486.11933
5926.513.359.380.045.19817
702.958.225.615.430.686.034.516.522.859.20733
5820.000.000.000.000.00117
400.000.000.000.000.040.000.000.000.000.00433
572.734.460.134.529.91216
7.477.272.227.333.344.433.337.222.727.74731
562.000.000.000.000.00116
4.000.000.000.000.004.000.000.000.000.00431
551.522.999.175.814.12316
2.319.526.489.530.497.940.359.846.259.13231
541.520.515.952.206.12316
2.311.968.760.913.292.923.190.678.691.13231
53211.877.852.724.47115
44.892.224.475.132.623.157.442.229.84429
52200.000.000.000.00115
40.000.000.000.000.400.000.000.000.00429
51159.657.521.992.89315
25.490.524.328.911.111.982.342.509.45229
50145.112.248.387.50315
21.057.564.632.076.367.023.646.575.01229
4927.276.194.939.18814
743.990.810.360.585.063.018.099.34727
4820.000.000.000.00114
400.000.000.000.040.000.000.000.00427
472.201.668.436.94113
4.847.343.906.222.226.093.437.48425
462.006.428.407.60113
4.025.754.954.828.284.594.575.20425
452.000.000.000.00113
4.000.000.000.004.000.000.000.00425
44312.477.762.97412
Prime!    97.642.352.353.235.325.324.67923
43200.000.000.00112
40.000.000.000.400.000.000.00423
42175.791.724.53012
30.902.730.413.231.403.720.90323
41170.460.122.78312
29.056.653.459.195.435.665.09223
40160.164.390.40712
25.652.631.954.445.913.625.65223
3920.000.000.00111
400.000.000.040.000.000.00421
3817.038.650.78311
290.315.620.505.026.513.09221
372.196.849.65910
4.826.148.424.248.416.28419
362.020.653.09910
4.083.038.946.498.303.80419
352.011.953.70110
4.047.957.694.967.597.40419
342.000.000.00110
4.000.000.004.000.000.00419
331.750.740.84010
3.065.093.488.843.905.60319
321.745.447.58010
3.046.587.254.527.856.40319
311.582.907.50710
2.505.596.175.716.955.05219
30287.490.3259
82.650.686.968.605.62817
29276.529.5929
76.468.615.251.686.46717
28201.146.4519
40.459.894.749.895.40417
27200.000.0019
40.000.000.400.000.00417
26174.546.0809
30.466.334.043.366.40317
2520.104.2998
404.182.838.281.40415
2420.000.0018
400.000.040.000.00415
232.808.6227
7.888.357.538.88713
22Prime!    2.211.1097
4.889.003.009.88413
212.000.0017
4.000.004.000.00413
20200.0016
40.000.400.00411
19167.3136
27.993.639.97211
18165.8376
27.501.910.57211
17152.1276
23.142.624.13211
16145.7976
21.256.765.21211
1531.6145
999.444.9999
1430.5065
Prime!    930.616.0399
1321.1295
446.434.6449
1220.0015
400.040.0049
112.8754
8.265.6287
102.0014
4.004.0047
93063
93.6395
82013
40.4045
71473
21.6125
6282
Prime!    7873
5212
4443
4Prime!    172
2923
3Prime!    21
Prime!    71
211
41
101
Prime!    31

[SQ4] Case X = 4
One can find the regular numbers of the form n2 + 4 at
%N n^2 + 4. under A087475.
The palindromic numbers of the form n2 + 4 are categorised as follows :
%N n^2 + 4 is a palindrome. under A0?????.
%N Palindromes of the form n^2 + 4. under A0?????.

More terms from Robert Xiao, Nov 11, 2022. See Index Nrs 87 up to 121.
More terms from Robert Xiao, Dec 6, 2022. See Index Nrs 122 up to 164.
More terms from Patrick De Geest, Jun 19, 2023. See Index Nrs 165 up to 174.
More terms from Patrick De Geest, Jul 14, 2023. See Index Nrs 175 up to 188.
1882.900.001.099.989.001.099.989.000.01228
8.410.006.379.937.416.355.738.741.021.201.478.375.536.147.399.736.000.14855
1872.900.000.109.999.890.000.109.999.98828
8.410.000.637.999.374.100.613.799.966.699.973.160.014.739.997.360.000.14855
1862.900.000.109.998.910.999.890.000.01228
8.410.000.637.993.695.899.122.421.231.321.242.219.985.963.997.360.000.14855
1852.900.000.109.890.000.109.890.000.01228
8.410.000.637.362.012.713.174.124.221.224.214.713.172.102.637.360.000.14855
1842.900.000.010.999.890.001.099.999.98828
8.410.000.063.799.362.127.377.579.966.699.757.737.212.639.973.600.000.14855
1832.900.000.010.890.000.108.900.000.01228
8.410.000.063.162.000.750.212.102.441.442.012.120.570.002.613.600.000.14855
1822.900.000.001.099.999.989.000.000.01228
8.410.000.006.379.999.937.410.000.045.400.000.147.399.999.736.000.000.14855
1812.900.000.000.109.999.890.000.000.01228
8.410.000.000.637.999.362.012.100.045.400.012.102.639.997.360.000.000.14855
1802.900.000.000.010.998.900.000.000.01228
8.410.000.000.063.793.620.000.121.045.401.210.000.263.973.600.000.000.14855
1792.900.000.000.001.089.000.000.000.01228
8.410.000.000.006.316.200.000.001.255.521.000.000.026.136.000.000.000.14855
1782.900.000.000.000.109.999.999.999.98828
8.410.000.000.000.637.999.999.999.942.499.999.999.997.360.000.000.000.14855
1772.900.000.000.000.000.000.000.000.01228
8.410.000.000.000.000.000.000.000.069.600.000.000.000.000.000.000.000.14855
1762.000.000.000.000.000.000.000.000.00028
4.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.00455
1751.831.250.807.788.962.715.512.898.22728
3.353.479.521.027.728.468.574.274.760.674.724.758.648.277.201.259.743.53355
174296.686.645.911.931.861.194.461.07827
88.022.965.862.472.034.564.400.419.091.400.446.543.027.426.856.922.08853
173290.000.109.998.901.099.989.000.01227
84.100.063.799.374.737.751.863.212.121.236.815.773.747.399.736.000.14853
172290.000.109.989.000.109.989.000.01227
84.100.063.793.632.161.373.765.202.120.256.737.316.123.639.736.000.14853
171290.000.010.998.901.099.890.000.01227
84.100.006.379.362.758.912.025.412.121.452.021.985.726.397.360.000.14853
170290.000.000.109.999.989.000.000.01227
84.100.000.063.799.993.632.100.004.540.000.123.639.999.736.000.000.14853
169290.000.000.010.999.890.000.000.01227
84.100.000.006.379.936.200.121.004.540.012.100.263.997.360.000.000.14853
168290.000.000.001.098.900.000.000.01227
84.100.000.000.637.362.000.001.214.541.210.000.026.373.600.000.000.14853
167290.000.000.000.000.000.000.000.01227
84.100.000.000.000.000.000.000.006.960.000.000.000.000.000.000.000.14853
166200.000.000.000.000.000.000.000.00027
40.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.00453
165187.231.510.560.684.573.900.386.24327
35.055.638.546.835.739.124.519.003.130.091.542.193.753.864.583.655.05353
16430.375.969.289.895.542.645.053.53526
922.699.510.300.677.117.288.074.010.470.882.711.776.003.015.996.22951
16329.000.010.998.900.109.989.000.01226
841.000.637.936.327.355.165.630.212.036.561.553.723.639.736.000.14851
16229.000.001.099.989.000.109.999.98826
841.000.063.799.363.216.355.799.666.997.553.612.363.997.360.000.14851
16129.000.001.098.900.109.890.000.01226
841.000.063.736.207.581.201.452.212.254.102.185.702.637.360.000.14851
16029.000.000.109.999.998.900.000.01226
841.000.006.379.999.948.300.000.454.000.003.849.999.973.600.000.14851
15929.000.000.109.989.001.099.999.98826
841.000.006.379.362.075.897.579.666.975.798.570.263.973.600.000.14851
15829.000.000.010.999.989.000.000.01226
841.000.000.637.999.362.121.000.454.000.121.263.999.736.000.000.14851
15729.000.000.001.099.890.000.000.01226
841.000.000.063.793.620.001.210.454.012.100.026.397.360.000.000.14851
15629.000.000.000.108.900.000.000.01226
841.000.000.006.316.200.000.012.555.210.000.002.613.600.000.000.14851
15529.000.000.000.010.999.999.999.98826
841.000.000.000.637.999.999.999.424.999.999.999.736.000.000.000.14851
15429.000.000.000.000.000.000.000.01226
841.000.000.000.000.000.000.000.696.000.000.000.000.000.000.000.14851
15320.000.000.000.000.000.000.000.00026
400.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.00451
15218.786.173.250.918.594.626.509.05726
352.920.305.413.529.318.101.080.191.080.101.813.925.314.503.029.25351
1512.900.001.098.900.010.989.000.01225
8.410.006.373.621.271.317.434.221.224.347.131.721.263.736.000.14849
1502.900.000.108.900.010.890.000.01225
8.410.000.631.620.075.021.212.441.442.121.205.700.261.360.000.14849
1492.900.000.010.999.998.900.000.01225
8.410.000.063.799.993.741.000.045.400.001.473.999.973.600.000.14849
1482.900.000.001.099.989.000.000.01225
8.410.000.006.379.936.201.210.045.400.121.026.399.736.000.000.14849
1472.900.000.000.109.890.000.000.01225
8.410.000.000.637.362.000.012.145.412.100.002.637.360.000.000.14849
1462.900.000.000.000.000.000.000.01225
8.410.000.000.000.000.000.000.069.600.000.000.000.000.000.000.14849
1452.016.406.378.989.886.382.871.84025
4.065.894.685.231.105.316.816.131.316.186.135.011.325.864.985.60449
1442.000.000.000.000.000.000.000.00025
4.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.00449
143303.369.241.034.269.972.962.05524
92.032.896.405.708.992.374.352.725.347.329.980.750.469.823.02947
142290.001.099.890.010.998.900.01224
84.100.637.937.416.137.398.302.120.389.373.161.473.973.600.14847
141290.000.109.998.900.010.999.98824
84.100.063.799.374.106.137.996.669.973.160.147.399.736.000.14847
140290.000.109.989.109.989.000.01224
84.100.063.793.695.891.224.323.132.342.219.859.639.736.000.14847
139290.000.010.998.900.109.999.98824
84.100.006.379.362.184.775.796.669.757.748.126.397.360.000.14847
138290.000.001.099.998.900.000.01224
84.100.000.637.999.363.210.004.540.001.236.399.973.600.000.14847
137290.000.000.109.989.000.000.01224
84.100.000.063.793.620.012.104.540.121.002.639.736.000.000.14847
136290.000.000.010.890.000.000.01224
84.100.000.006.316.200.000.125.552.100.000.261.360.000.000.14847
135290.000.000.001.099.999.999.98824
84.100.000.000.637.999.999.994.249.999.999.973.600.000.000.14847
134290.000.000.000.000.000.000.01224
84.100.000.000.000.000.000.006.960.000.000.000.000.000.000.14847
133238.544.802.011.526.217.603.71924
56.903.622.566.718.242.592.308.980.329.524.281.766.522.630.96547
132200.000.000.000.000.000.000.00024
40.000.000.000.000.000.000.000.000.000.000.000.000.000.000.00447
131197.673.081.468.710.223.099.78324
39.074.647.137.335.349.012.352.225.321.094.353.373.174.647.09347
13029.418.554.617.804.321.568.25823
865.451.355.800.735.972.660.505.066.279.537.008.553.154.56845
12929.000.109.989.010.998.900.01223
841.006.379.374.735.518.741.212.147.815.537.473.973.600.14845
12829.000.010.989.010.989.000.01223
841.000.637.362.758.120.363.212.363.021.857.263.736.000.14845
12729.000.001.099.999.890.000.01223
841.000.063.799.994.830.000.454.000.038.499.997.360.000.14845
12629.000.000.109.998.900.000.01223
841.000.006.379.936.212.100.454.001.212.639.973.600.000.14845
12529.000.000.010.989.000.000.01223
841.000.000.637.362.000.121.454.121.000.263.736.000.000.14845
12429.000.000.000.000.000.000.01223
841.000.000.000.000.000.000.696.000.000.000.000.000.000.14845
12320.120.856.920.402.995.479.78023
404.848.883.211.329.115.176.282.671.511.923.112.388.848.40445
12220.000.000.000.000.000.000.00023
400.000.000.000.000.000.000.000.000.000.000.000.000.000.00445
1213.037.257.927.764.768.671.81522
9.224.935.719.769.936.751.167.611.576.399.679.175.394.22943
1202.902.181.234.697.473.764.16222
8.422.655.919.030.153.295.603.065.923.510.309.195.562.24843
1192.900.010.989.001.098.900.01222
8.410.063.736.327.131.765.221.225.671.317.236.373.600.14843
1182.900.001.099.890.010.999.98822
8.410.006.379.363.273.557.966.697.553.723.639.736.000.14843
1172.900.001.089.001.089.000.01222
8.410.006.316.207.502.123.441.443.212.057.026.136.000.14843
1162.900.000.109.999.890.000.01222
8.410.000.637.999.374.100.045.400.014.739.997.360.000.14843
1152.900.000.010.998.900.000.01222
8.410.000.063.793.620.121.045.401.210.263.973.600.000.14843
1142.900.000.001.089.000.000.01222
8.410.000.006.316.200.001.255.521.000.026.136.000.000.14843
1132.900.000.000.109.999.999.98822
8.410.000.000.637.999.999.942.499.999.997.360.000.000.14843
1122.900.000.000.000.000.000.01222
8.410.000.000.000.000.000.069.600.000.000.000.000.000.14843
1112.417.752.415.892.977.285.94122
5.845.526.744.556.328.205.045.405.028.236.554.476.255.48543
1102.255.544.112.617.592.637.34922
5.087.479.243.963.883.417.955.597.143.883.693.429.747.80543
1092.000.000.000.000.000.000.00022
4.000.000.000.000.000.000.000.000.000.000.000.000.000.00443
1081.878.789.543.471.386.049.05722
3.529.850.148.657.419.208.590.958.029.147.568.410.589.25343
107294.476.198.109.761.765.04221
86.716.231.253.179.658.522.722.585.697.135.213.261.76841
106290.000.010.999.890.000.01221
84.100.006.379.936.321.004.540.012.363.997.360.000.14841
105290.000.001.098.900.000.01221
84.100.000.637.362.001.214.541.210.026.373.600.000.14841
104290.000.000.000.000.000.01221
84.100.000.000.000.000.006.960.000.000.000.000.000.14841
103232.569.949.504.501.382.17921
54.088.781.412.526.322.702.120.722.362.521.418.788.04541
102200.000.000.000.000.000.00021
40.000.000.000.000.000.000.000.000.000.000.000.000.00441
10129.000.109.989.001.099.98820
841.006.379.374.161.379.666.973.161.473.973.600.14839
10029.000.109.891.098.900.01220
841.006.373.695.812.254.313.452.218.596.373.600.14839
9929.000.010.999.989.000.01220
841.000.637.999.483.000.454.000.384.999.736.000.14839
9829.000.010.989.010.999.98820
841.000.637.362.758.757.666.757.857.263.736.000.14839
9729.000.001.099.890.000.01220
841.000.063.793.621.210.454.012.126.397.360.000.14839
9629.000.000.108.900.000.01220
841.000.006.316.200.012.555.210.002.613.600.000.14839
9529.000.000.010.999.999.98820
841.000.000.637.999.999.424.999.999.736.000.000.14839
9429.000.000.000.000.000.01220
841.000.000.000.000.000.696.000.000.000.000.000.14839
9320.000.000.000.000.000.00020
400.000.000.000.000.000.000.000.000.000.000.000.00439
922.900.109.890.109.890.01219
8.410.637.374.713.198.321.238.913.174.737.360.14837
912.900.010.890.108.900.01219
8.410.063.162.750.214.541.454.120.572.613.600.14837
902.900.001.099.989.000.01219
8.410.006.379.937.410.045.400.147.399.736.000.14837
892.900.000.109.890.000.01219
8.410.000.637.362.012.145.412.102.637.360.000.14837
882.900.000.000.000.000.01219
8.410.000.000.000.000.069.600.000.000.000.000.14837
872.000.000.000.000.000.00019
4.000.000.000.000.000.000.000.000.000.000.000.00437
86290.001.098.901.099.98818
84.100.637.363.845.576.667.554.836.373.600.14835
85290.000.109.989.000.01218
84.100.063.793.632.104.540.123.639.736.000.14835
84290.000.010.890.000.01218
84.100.006.316.200.125.552.100.261.360.000.14835
83290.000.001.099.999.98818
84.100.000.637.999.994.249.999.973.600.000.14835
82290.000.000.000.000.01218
84.100.000.000.000.006.960.000.000.000.000.14835
81284.408.918.191.650.29818
80.888.432.746.944.831.813.844.964.723.488.80835
80200.000.000.000.000.00018
40.000.000.000.000.000.000.000.000.000.000.00435
7930.367.729.387.366.71517
922.198.988.144.335.999.533.441.889.891.22933
7829.000.109.998.900.01217
841.006.379.948.300.454.003.849.973.600.14833
7729.000.010.989.000.01217
841.000.637.362.121.454.121.263.736.000.14833
7629.000.000.000.000.01217
841.000.000.000.000.696.000.000.000.000.14833
7520.000.000.000.000.00017
400.000.000.000.000.000.000.000.000.000.00433
7419.271.985.571.352.23717
Prime!    371.409.427.862.408.808.804.268.724.904.17333
732.900.109.890.109.98816
8.410.637.374.713.766.673.174.737.360.14831
722.900.108.910.890.01216
8.410.631.695.023.651.563.205.961.360.14831
712.900.010.998.900.01216
8.410.063.793.741.045.401.473.973.600.14831
702.900.010.891.099.98816
8.410.063.168.498.546.458.948.613.600.14831
692.900.001.089.000.01216
8.410.006.316.201.255.521.026.136.000.14831
682.900.000.109.999.98816
8.410.000.637.999.942.499.997.360.000.14831
672.900.000.000.000.01216
8.410.000.000.000.069.600.000.000.000.14831
662.000.000.000.000.00016
4.000.000.000.000.000.000.000.000.000.00431
65290.001.098.900.01215
84.100.637.363.214.541.236.373.600.14829
64290.000.000.000.01215
84.100.000.000.006.960.000.000.000.14829
63225.116.991.118.80115
50.677.659.690.382.328.309.695.677.60529
62200.000.000.000.00015
40.000.000.000.000.000.000.000.000.00429
6129.001.099.890.01214
841.063.794.830.454.038.497.360.14827
6029.001.089.109.98814
841.063.169.565.464.565.961.360.14827
5929.000.108.900.01214
841.006.316.212.555.212.613.600.14827
5829.000.010.999.98814
841.000.637.999.424.999.736.000.14827
5729.000.000.000.01214
841.000.000.000.696.000.000.000.14827
5624.096.294.452.00914
580.631.406.317.919.713.604.136.08527
5523.283.121.322.42114
542.103.738.514.575.415.837.301.24527
5420.102.019.998.52014
404.091.208.020.898.020.802.190.40427
5320.000.000.000.00014
400.000.000.000.000.000.000.000.00427
5217.784.936.509.39714
316.303.966.643.282.346.669.303.61327
512.900.109.890.01213
8.410.637.374.145.414.737.360.14825
502.900.000.000.01213
8.410.000.000.069.600.000.000.14825
492.000.000.000.00013
4.000.000.000.000.000.000.000.00425
481.893.180.648.20713
3.584.132.966.745.476.692.314.85325
47291.098.901.08812
84.738.570.214.641.207.583.74823
46290.010.890.01212
84.106.316.325.552.361.360.14823
45290.001.099.98812
84.100.637.994.249.973.600.14823
44290.000.000.01212
84.100.000.006.960.000.000.14823
43234.304.304.47112
54.898.507.093.639.070.589.84523
42200.000.000.00012
40.000.000.000.000.000.000.00423
4129.010.989.01211
841.637.483.454.384.736.14821
4029.000.000.01211
841.000.000.696.000.000.14821
3920.046.487.91011
401.861.677.525.776.168.10421
3820.000.000.00011
400.000.000.000.000.000.00421
372.901.089.01210
8.416.317.455.547.136.14819
362.900.109.98810
8.410.637.942.497.360.14819
352.900.000.01210
8.410.000.069.600.000.14819
342.418.272.55910
5.848.042.169.612.408.48519
332.000.000.00010
4.000.000.000.000.000.00419
321.981.904.48310
Prime!    3.927.945.379.735.497.29319
31293.695.2929
86.256.924.542.965.26817
30291.098.9129
84.738.576.567.583.74817
29290.000.0129
84.100.006.960.000.14817
28200.000.0009
40.000.000.000.000.00417
27Prime!    197.605.7179
39.048.019.391.084.09317
26177.437.6539
31.484.120.702.148.41317
2529.108.9128
847.328.757.823.74815
2429.010.9888
841.637.424.736.14815
2329.000.0128
841.000.696.000.14815
2224.208.2918
586.041.353.140.68515
2123.020.9118
529.962.343.269.92515
2020.000.0008
400.000.000.000.00415
192.900.0127
8.410.069.600.14813
182.000.0007
4.000.000.000.00413
17291.0886
84.732.223.74811
16290.0126
84.106.960.14811
15284.2986
80.825.352.80811
14200.0006
40.000.000.00411
1329.0125
841.696.1489
1220.2305
409.252.9049
1120.0005
400.000.0049
102.9124
8.479.7487
92.3694
5.612.1657
82.3294
5.424.2457
72.0004
4.000.0047
6Prime!    2413
58.0855
52003
40.0045
4202
4043
3Prime!    21
81
211
Prime!    51
101
41

[SQ5] Case X = 5
One can find the regular numbers of the form n2 + 5 at
%N n^2 + 5. under A117951.
The palindromic numbers of the form n2 + 5 are categorised as follows :
%N n^2 + 5 is a palindrome. under A0?????.
%N Palindromes of the form n^2 + 5. under A0?????.

More terms from Robert Xiao, Nov 11, 2022. See Index Nrs 58 up to 65.
More terms from Robert Xiao, Dec 6, 2022. See Index Nrs 66 up to 76.
More terms from Patrick De Geest, Jun 19, 2023. See Index Nrs 77 up to 80.
More terms from Patrick De Geest, Jul 14, 2023. See Index Nrs 81 up to 84.
842.608.317.961.925.849.997.301.962.74128
6.803.322.590.505.019.876.166.220.133.310.226.616.789.105.050.952.233.08655
832.236.172.763.728.034.518.014.769.20028
5.000.468.629.239.076.088.946.953.692.963.596.498.806.709.329.268.640.00555
822.170.611.886.701.992.339.601.411.48728
4.711.555.962.691.982.828.932.337.796.977.332.398.282.891.962.695.551.17455
811.024.732.804.781.701.605.349.281.36428
1.050.077.321.195.772.972.492.798.382.838.972.942.792.775.911.237.700.50155
80303.377.367.327.121.047.407.126.96827
92.037.827.006.334.933.212.320.892.829.802.321.233.943.360.072.873.02953
79225.625.257.500.999.442.452.503.97027
50.906.756.822.392.305.171.406.278.387.260.417.150.329.322.865.760.90553
78213.086.534.693.100.234.730.094.85727
45.405.871.267.513.809.946.832.612.521.623.864.990.831.576.217.850.45453
77102.129.649.837.038.452.874.956.91427
10.430.465.375.836.088.483.878.152.625.187.838.488.063.857.356.403.40153
7630.491.299.440.459.413.362.323.38226
929.719.341.567.760.534.394.889.969.988.493.435.067.765.143.917.92951
7511.940.382.254.619.255.930.927.89426
142.572.728.386.426.425.573.054.828.450.375.524.624.683.827.275.24151
742.545.742.927.821.310.225.739.97125
6.480.807.054.552.216.725.775.159.515.775.276.122.554.507.080.84649
732.181.250.445.404.125.929.298.66325
4.757.853.505.575.697.751.400.812.180.041.577.965.755.053.587.57449
722.126.498.177.863.018.518.342.05725
4.521.994.500.454.737.941.688.051.508.861.497.374.540.054.991.25449
711.019.436.539.921.314.058.049.03625
1.039.250.858.926.740.951.187.928.297.811.590.476.298.580.529.30149
70253.085.558.532.147.564.089.92924
64.052.299.937.529.090.675.261.916.257.609.092.573.999.225.04647
6924.579.729.990.136.793.435.70123
604.163.126.388.030.091.527.888.725.190.030.883.621.361.40645
6813.611.551.440.257.265.885.97623
185.274.332.610.769.649.281.505.182.946.967.016.233.472.58145
6711.323.759.642.883.772.885.89623
128.227.532.449.803.231.640.787.046.132.308.944.235.722.82145
6610.428.491.102.191.924.045.78623
108.753.426.668.496.130.811.515.118.031.694.866.624.357.80145
652.215.443.702.838.748.706.71722
4.908.190.800.447.865.884.417.144.885.687.440.080.918.09443
64Prime!    2.127.607.768.307.889.069.55722
4.526.714.815.764.076.176.238.326.716.704.675.184.176.25443
63219.053.063.944.547.317.43721
47.984.244.823.493.935.958.185.953.939.432.844.248.97441
6231.090.052.146.796.100.89220
966.591.342.490.500.841.808.148.005.094.243.195.66939
6125.314.091.916.443.521.57120
640.803.249.554.151.242.686.242.151.455.942.308.04639
603.069.968.682.528.960.33819
9.424.707.711.708.600.467.640.068.071.177.074.24937
593.013.786.952.525.175.70219
9.082.911.795.210.985.660.665.890.125.971.192.80937
582.171.105.566.696.549.48719
4.713.699.381.740.745.292.925.470.471.839.963.17437
57311.023.143.446.721.95818
96.735.395.759.480.184.048.108.495.759.353.76935
5622514845711723986018
50.691.827.742.273.596.169.537.224.772.819.60535
55222.757.722.839.648.61718
49.621.003.084.705.711.111.750.748.030.012.69435
5430.165.492.872.565.64817
909.956.960.244.808.909.808.442.069.659.90933
5312.873.477.448.137.33417
165.726.421.607.700.525.007.706.124.627.56133
5210.337.004.802.295.31417
106.853.668.282.676.383.676.282.866.358.60133
512.608.645.939.541.25916
6.805.033.637.885.097.905.887.363.305.08631
502.505.030.843.903.93916
6.275.179.528.910.080.800.198.259.715.72631
492.245.985.885.884.62016
5.044.452.599.592.921.292.959.952.544.40531
482.215.491.736.254.53316
4.908.403.633.412.125.212.143.363.048.09431
471.279.111.244.371.43416
1.636.125.575.477.438.347.745.755.216.36131
461.128.636.081.957.65416
1.273.819.405.496.724.276.945.049.183.72131
451.108.041.335.154.09616
1.227.755.600.410.071.700.140.065.577.22131
44309.910.900.890.99215
96.044.766.491.066.266.019.466.744.06929
43262.407.097.891.85915
68.857.485.024.027.672.042.058.475.88629
42204.099.968.332.39715
41.656.797.073.285.458.237.079.765.61429
41120.984.198.909.69415
14.637.176.385.820.402.858.367.173.64129
40120.357.148.031.79415
14.485.843.082.347.174.328.034.858.44129
39112.770.894.443.84615
12.717.274.633.665.056.633.647.271.72129
3831.090.089.099.10814
966.593.640.190.474.091.046.395.66927
3730.990.990.990.99214
960.441.522.603.747.306.225.144.06927
3625.763.006.263.48114
663.732.491.732.161.237.194.237.36627
3512.686.342.618.41614
160.943.289.031.838.130.982.349.06127
343.048.771.427.88213
9.295.007.219.469.649.127.005.92925
332.256.574.603.77013
5.092.128.942.379.732.498.212.90525
32309.910.890.99212
96.044.760.355.455.306.744.06923
31225.101.642.74012
50.670.749.564.246.594.707.60523
30218.488.832.63712
47.737.369.987.078.996.373.77423
29214.091.717.95712
45.835.263.697.779.636.253.85423
2830.990.990.99211
960.441.522.666.225.144.06921
2722.360.694.00011
500.000.636.161.636.000.00521
2612.996.564.68411
Prime!    168.910.693.585.396.019.86121
253.108.910.89210
9.665.326.934.396.235.66919
243.099.109.00810
9.604.476.643.466.744.06919
233.049.566.11810
9.299.853.508.053.589.92919
222.172.438.48710
4.719.488.979.798.849.17419
21Prime!    2.171.728.98710
4.716.406.792.976.046.17419
20310.900.8929
96.659.364.646.395.66917
19307.606.2629
94.621.612.421.612.64917
18204.050.6039
41.636.648.584.663.61417
17203.480.3479
41.404.251.615.240.41417
1631.089.1088
966.532.636.235.66915
1530.990.9928
960.441.585.144.06915
1424.619.1998
606.104.959.401.60615
1320.920.2778
437.657.989.756.73415
1213.778.3248
189.842.212.248.98115
111.007.4367
1.014.927.294.10113
10310.8926
96.653.835.66911
9136.4746
18.625.152.68111
822.5705
509.404.9059
7Prime!    20.3475
414.000.4149
61.3744
1.887.8817
51.0144
Prime!    1.028.2017
42033
41.2145
3Prime!    21
91
211
61
101
Prime!    51

[SQ6] Case X = 6
One can find the regular numbers of the form n2 + 6 at
%N n^2 + 6. under A114949.
The palindromic numbers of the form n2 + 6 are categorised as follows :
%N n^2 + 6 is a palindrome. under A0?????.
%N Palindromes of the form n^2 + 6. under A0?????.

More terms from Robert Xiao, Nov 11, 2022. See Index Nrs 61 up to 82.
More terms from Robert Xiao, Dec 6, 2022. See Index Nrs 83 up to 97.
More terms from Patrick De Geest, Jun 19, 2023. See Index Nrs 98 up to 100.
More terms from Patrick De Geest, Jul 14, 2023. See Index Nr 101.
1011.168.357.463.116.717.194.901.869.92528
1.365.059.161.620.531.180.461.673.462.643.761.640.811.350.261.619.505.63155
100273.173.989.414.061.594.450.934.12127
74.624.028.492.393.836.067.170.881.218.807.176.063.839.329.482.042.64753
99265.038.553.079.107.447.261.115.85127
70.245.434.618.266.855.713.477.904.840.977.431.755.866.281.643.454.20753
98244.963.216.756.609.262.282.078.60027
60.006.977.563.745.532.860.468.521.812.586.406.823.554.736.577.960.00653
9715.148.395.492.186.361.434.190.94626
229.473.885.987.692.075.483.196.292.691.384.570.296.789.588.374.92251
9611.445.307.918.118.190.724.792.34526
130.995.073.340.538.953.200.613.939.316.002.359.835.043.370.599.03151
957.735.028.286.407.992.258.395.41725
59.830.662.591.531.761.114.481.600.618.441.116.713.519.526.603.89550
945.321.287.107.431.121.496.335.37625
28.316.096.479.712.671.969.185.833.858.196.917.621.797.469.061.38250
932.449.580.393.484.490.046.253.80025
6.000.444.104.143.629.085.048.673.768.405.809.263.414.014.440.00649
922.442.550.312.397.786.875.460.38325
5.966.052.028.594.526.257.688.761.678.867.526.254.958.202.506.69549
912.442.026.223.593.354.633.854.88325
5.963.492.076.717.620.880.176.445.446.710.880.267.176.702.943.69549
902.304.770.226.844.800.778.293.87725
5.311.965.798.550.234.438.140.397.930.418.344.320.558.975.691.13549
892.277.550.911.878.787.903.106.30325
5.187.238.156.199.898.300.363.348.433.630.038.989.916.518.327.81549
88837.032.925.807.939.639.181.75124
700.624.118.886.599.784.468.257.752.864.487.995.688.811.426.00748
87360.704.162.727.349.635.589.10524
130.107.493.008.838.326.101.384.483.101.623.838.800.394.701.03148
86244.951.188.117.043.639.740.10024
60.001.084.559.951.301.218.062.226.081.210.315.995.548.010.00647
8587.720.196.541.627.213.013.28123
7.694.832.881.301.706.862.277.557.722.686.071.031.882.384.96746
8424.496.817.828.977.404.825.70023
600.094.083.746.105.253.503.717.305.352.501.647.380.490.00645
8314.868.460.878.669.856.533.45423
221.071.128.900.536.002.207.515.702.200.635.009.821.170.12245
828.417.172.441.256.183.012.40122
70.848.791.905.842.571.664.733.746.617.524.850.919.784.80744
815.163.840.052.719.535.907.28422
26.665.244.090.070.499.378.288.287.399.407.009.044.256.66244
803.634.330.070.670.024.646.01522
13.208.355.062.576.386.337.755.773.368.367.526.055.380.23144
791.554.199.320.080.257.271.05622
2.415.535.526.537.933.992.207.022.993.397.356.255.355.14243
781.150.718.169.375.159.504.18522
1.324.152.305.330.118.276.618.166.728.110.335.032.514.23143
77280.164.221.747.072.237.94121
78.491.991.147.142.664.705.050.746.624.174.119.919.48741
76170.130.929.266.558.655.32421
28.944.533.093.102.784.397.579.348.720.139.033.544.98241
75162.770.842.413.479.976.88421
26.494.347.139.993.932.146.064.123.939.993.174.349.46241
74143.036.040.013.751.791.58621
20.459.308.742.815.603.622.922.630.651.824.780.395.40241
7387.618.786.932.287.637.31920
7.677.051.823.485.618.838.558.388.165.843.281.507.76740
7245.308.376.470.692.112.13620
2.052.848.978.409.966.615.335.166.699.048.798.482.50240
7136.446.586.270.502.176.13520
1.328.353.650.773.157.724.554.277.513.770.563.538.23140
7024.628.145.541.292.686.16020
606.545.552.803.094.817.373.718.490.308.255.545.60639
6924.582.269.106.998.462.32020
604.287.954.448.890.978.121.879.098.844.459.782.40639
6816.155.300.870.112.580.91620
260.993.746.203.860.314.040.413.068.302.647.399.06239
677.809.375.058.123.238.67019
60.986.338.798.437.337.355.373.373.489.783.368.90638
662.439.148.944.350.323.81719
5.949.447.572.725.299.072.709.925.272.757.449.49537
651.677.636.982.898.559.27619
2.814.465.846.388.980.868.680.898.836.485.644.18237
641.560.218.119.907.775.15619
2.434.280.581.688.552.654.562.558.861.850.824.34237
631.168.570.781.579.457.07519
1.365.557.671.561.223.174.713.221.651.767.555.63137
621.151.500.037.540.011.51519
1.325.952.336.454.647.928.297.464.546.332.595.23137
611.140.785.636.737.247.89519
1.301.391.868.986.008.114.118.006.898.681.931.03137
60518.382.838.739.954.31618
268.720.767.500.093.481.184.390.005.767.027.86236
59453.688.870.735.185.13618
205.833.591.428.967.527.725.769.824.195.338.50236
58Prime!    275.918.682.887.508.13118
76.131.119.566.377.272.327.277.366.591.113.16735
57272.826.851.328.266.52118
74.434.490.805.696.043.534.069.650.809.443.44735
56230.953.456.951.103.17718
53.339.499.277.665.068.386.056.677.299.493.33535
55150.456.252.387.445.79618
22.637.083.882.474.788.788.747.428.838.073.62235
54114.180.351.500.147.05518
13.037.152.668.697.133.833.179.686.625.173.03135
5324.683.119.453.972.73017
609.256.385.979.087.040.780.979.583.652.90633
5224.389.266.701.248.93317
594.836.330.224.650.010.056.422.033.638.49533
5123.622.123.718.428.45717
558.004.728.968.740.272.047.869.827.400.85533
5016.142.690.249.866.41617
260.586.448.503.132.252.231.305.844.685.06233
4914.480.123.530.112.33617
209.673.977.447.312.939.213.744.779.376.90233
482.773.554.286.001.03116
7.692.603.377.394.688.864.937.733.062.96731
471.140.454.064.936.00516
1.300.635.474.229.057.509.224.745.360.03131
46455.835.912.156.23615
207.786.378.811.307.703.118.873.687.70230
45114.028.867.547.99515
13.002.582.634.278.187.243.628.520.03129
4427.668.521.984.58114
765.547.108.811.242.118.801.745.56727
431.622.457.383.43413
2.632.367.961.059.501.697.632.36225
42360.616.362.24512
130.044.160.718.817.061.440.03124
41234.732.340.24312
55.099.271.555.955.517.299.05523
40162.829.334.66612
26.513.392.227.772.229.331.56223
39157.495.523.40612
24.804.839.892.929.893.840.84223
38157.302.301.85612
24.744.014.169.196.141.044.74223
37144.260.002.21412
20.810.948.238.783.284.901.80223
3636.131.148.25511
1.305.459.874.224.789.545.03122
3528.043.323.45911
Prime!    786.427.990.626.099.724.68721
3427.979.618.65911
782.859.060.303.060.958.28721
333.645.161.86510
13.287.205.022.050.278.23120
322.354.704.14310
5.544.631.601.061.364.45519
311.554.076.05610
2.415.152.387.832.515.14219
30360.581.0059
130.018.661.166.810.03118
29156.832.7449
24.596.509.590.569.54217
28144.402.2869
20.852.020.202.025.80217
2788.574.6918
7.845.475.885.745.48716
2624.589.4208
604.639.575.936.40615
2523.954.0378
573.795.888.597.37515
2416.963.9248
287.774.717.477.78215
2311.504.3658
132.350.414.053.23115
2211.493.7158
Prime!    132.105.484.501.23115
218.493.4897
72.139.355.393.12714
207.586.6637
57.557.455.475.57514
19245.8206
60.427.472.40611
18230.6236
53.186.968.13511
17169.8746
28.857.175.88211
16144.6646
20.927.672.90211
1586.3795
7.461.331.64710
1416.7765
281.434.1829
1315.5565
241.989.1429
1211.5155
Prime!    132.595.2319
11Prime!    2.7294
7.447.4477
101563
24.3425
91153
13.2315
8Prime!    732
5.3354
7Prime!    232
5353
6162
2623
5142
2023
4Prime!    71
552
341
222
211
Prime!    71
101
61

[SQ7] Case X = 7
One can find the regular numbers of the form n2 + 7 at
%N n^2 + 7. under A117619.
The palindromic numbers of the form n2 + 7 are categorised as follows :
%N n^2 + 7 is a palindrome. under A0?????.
%N Palindromes of the form n^2 + 7. under A0?????.

More terms from Robert Xiao, Nov 11, 2022. See Index Nrs 81 up to 96.
More terms from Robert Xiao, Dec 6, 2022. See Index Nrs 97 up to 126.
More terms from Patrick De Geest, Jun 19, 2023. See Index Nr 127.
More terms from Patrick De Geest, Jul 14, 2023. See Index Nrs 128 up to 130.
1302.942.490.700.903.630.114.322.781.08128
8.658.251.524.904.336.416.085.987.641.467.895.806.146.334.094.251.528.56855
1292.478.146.896.440.447.702.275.533.15328
6.141.212.040.337.423.028.682.883.418.143.882.868.203.247.330.402.121.41655
1281.056.191.645.307.124.757.182.258.15228
1.115.540.791.616.571.230.111.435.221.225.341.110.321.756.161.970.455.11155
127263.063.305.011.355.973.968.198.76727
69.202.302.443.497.705.087.265.623.232.656.278.050.779.434.420.320.29653
12691.099.471.205.452.388.400.727.16126
8.299.113.653.913.048.840.196.244.664.426.910.488.403.193.563.119.92852
12589.826.328.827.887.375.300.938.05126
8.068.769.350.695.750.527.079.826.336.289.707.250.575.960.539.678.60852
12454.860.391.716.211.667.125.652.11426
3.009.662.579.256.185.707.509.394.334.939.057.075.816.529.752.669.00352
12348.233.481.882.821.257.558.948.53526
2.326.468.774.540.446.485.104.673.883.764.015.846.440.454.778.646.23252
12225.507.794.461.096.521.574.660.99326
650.647.578.269.546.385.496.018.666.810.694.583.645.962.875.746.05651
12118.002.664.614.352.900.660.768.80426
324.095.933.216.874.073.471.884.070.488.174.370.478.612.339.590.42351
12017.356.411.272.825.497.206.341.43626
301.245.012.271.463.996.018.979.464.979.810.699.364.172.210.542.10351
11913.260.186.203.815.768.014.854.75826
175.832.538.159.866.028.760.516.999.615.067.820.668.951.835.238.57151
1184.402.892.896.272.656.542.280.37225
19.385.465.856.048.221.922.182.688.628.122.912.284.065.856.458.39150
1173.650.119.602.302.946.715.787.01825
13.323.373.111.116.221.895.403.211.230.459.812.261.111.137.332.33150
1162.835.877.657.806.853.273.490.04925
8.042.202.090.048.083.991.186.492.946.811.993.808.400.902.022.40849
1152.648.945.811.327.407.899.817.81025
7.016.913.911.349.019.290.528.586.858.250.929.109.431.193.196.10749
1141.959.041.911.761.241.619.235.87625
3.837.845.212.037.140.394.540.658.560.454.930.417.302.125.487.38349
1131.519.290.749.752.846.555.298.80525
2.308.244.382.284.566.615.330.760.670.335.166.654.822.834.428.03249
1121.091.474.696.085.899.725.847.64825
1.191.317.012.195.807.170.319.468.649.130.717.085.912.107.131.91149
111840.475.663.958.054.927.364.56024
706.399.341.705.733.270.452.160.061.254.072.337.507.143.993.60748
110387.986.913.317.087.808.021.36224
150.533.844.905.321.408.668.834.438.866.804.123.509.448.335.05148
109338.967.250.292.401.084.872.10224
114.898.796.770.791.283.357.724.427.753.382.197.077.697.898.41148
108287.611.379.055.115.254.754.56124
82.720.305.361.985.189.850.828.882.805.898.158.916.350.302.72847
107264.856.474.545.621.188.105.29024
70.148.952.108.735.284.340.218.181.204.348.253.780.125.984.10747
106264.769.196.952.694.343.976.49024
70.102.727.654.974.647.884.431.913.448.874.647.945.672.720.10747
105252.862.326.223.456.965.634.17324
63.939.356.023.137.972.232.251.115.223.227.973.132.065.393.93647
104186.223.280.118.662.403.492.30624
34.679.110.058.153.803.996.122.122.169.930.835.185.001.197.64347
103105.981.859.301.671.561.558.30224
11.232.154.501.039.306.893.769.296.739.860.393.010.545.123.21147
10260.027.803.545.710.884.744.58423
3.603.337.198.522.460.266.607.557.066.620.642.258.917.333.06346
10139.261.271.767.978.723.059.96223
1.541.447.460.839.083.126.373.553.736.213.809.380.647.441.45146
10028.289.596.381.987.023.979.74923
800.301.263.455.733.317.172.909.271.713.337.554.362.103.00845
9926.583.862.755.181.345.102.26023
706.701.758.986.317.896.644.575.446.698.713.689.857.107.60745
9825.202.778.524.929.009.945.22723
635.180.045.376.622.882.369.161.963.288.226.673.540.081.53645
9712.534.744.924.385.709.079.08823
157.119.830.319.413.295.618.626.816.592.314.913.038.911.75145
969.098.793.634.336.163.132.43922
82.788.045.600.236.283.894.955.949.838.263.200.654.088.72844
953.928.569.527.872.514.544.53822
15.433.658.535.328.471.832.833.823.817.482.353.585.633.45144
941.537.941.142.429.962.821.27522
2.365.262.957.578.779.188.923.298.819.778.757.592.625.63243
93819.654.924.304.049.136.98721
671.834.194.935.876.520.631.136.025.678.539.491.438.17642
92264.578.221.348.715.623.10021
Prime!    70.001.635.212.049.959.511.011.595.994.021.253.610.00741
91173.433.603.204.449.703.11421
30.079.214.720.478.506.328.482.360.587.402.741.297.00341
90138.919.426.155.524.877.27821
19.298.606.963.380.329.384.548.392.308.336.960.689.29141
8978.284.014.312.506.124.70320
6.128.386.896.880.663.780.330.873.660.886.986.838.21640
884.863.285.092.822.507.787520
2.365.154.189.406.962.818.668.182.696.049.814.515.63240
8733.461.809.521.528.188.34820
1.119.692.696.455.034.525.225.254.305.546.962.969.11140
8629.703.155.895.287.202.09120
882.277.470.139.734.867.989.768.437.931.074.772.28839
8525.663.014.005.115.285.29320
658.590.287.826.743.276.202.672.347.628.782.095.85639
8415.184.212.330.423.918.49520
230.560.304.095.397.765.777.567.793.590.403.065.03239
8310.598.512.776.880.704.19820
112.328.473.081.703.535.565.535.307.180.374.823.21139
825.481.862.572.563.901.61419
30.050.817.264.476.917.488.471.967.446.271.805.00338
814.796.766.642.213.991.75519
23.008.970.219.856.893.188.139.865.891.207.980.03238
80621.027.581.747.737.97618
385.675.257.291.443.374.473.344.192.752.576.58336
79265.381.792.368.454.18018
70.427.495.720.693.325.252.339.602.759.472.40735
78186.352.346.145.995.85618
34.727.196.914.117.056.565.071.141.969.172.74335
77175.384.862.900.595.23618
30.759.850.134.660.587.178.506.643.105.895.70335
76151.732.545.338.808.04518
23.022.765.314.993.438.983.439.941.356.722.03235
75123.558.432.548.360.16218
15.266.686.253.807.667.876.670.835.268.666.25135
74109.507.179.675.599.35218
11.991.822.400.503.999.799.930.500.422.819.91135
7382.414.649.436.802.81317
6.792.174.441.791.102.222.011.971.444.712.97634
7234.473.342.592.827.20217
1.188.411.349.522.434.114.342.259.431.148.81134
716.044.398.343.213.16616
36.534.751.331.438.066.083.413.315.743.56332
706.020.132.259.989.51616
36.241.992.427.766.477.466.772.429.914.26332
694.798.837.268.824.20516
23.028.839.132.656.155.165.623.193.882.03232
683.896.993.565.142.98816
15.186.558.846.765.855.856.764.885.568.15132
672.880.426.541.419.41116
8.296.857.060.513.389.833.150.607.586.92831
662.872.658.932.455.78916
8.252.169.342.218.033.308.122.439.612.52831
65928.397.928.617.61915
861.922.713.861.485.584.168.317.229.16830
64894.779.501.236.75115
800.630.355.833.488.884.338.553.036.00830
63390.478.814.572.83815
152.473.704.630.208.802.036.407.374.25130
62247.007.970.190.24715
61.012.937.337.505.950.573.373.921.01629
61139.767.782.028.82815
19.535.032.893.257.975.239.823.053.59129
60124.845.622.180.88815
15.586.429.377.733.033.777.392.468.55129
5926.346.484.384.43314
694.137.239.419.171.914.932.731.49627
5815.258.510.823.13514
232.822.152.539.727.935.251.228.23227
5711.545.204.077.98214
133.291.737.202.252.202.737.192.33127
568.372.856.137.01013
70.104.719.891.066.019.891.740.10726
558.356.234.672.33313
69.826.657.899.100.199.875.662.89626
548.309.775.585.96713
69.052.370.289.133.198.207.325.09626
533.693.414.147.56813
13.641.308.065.455.456.080.314.63126
521.065.362.822.95213
1.134.997.944.528.254.497.994.31125
51921.146.111.27912
848.510.158.324.423.851.015.84824
50899.067.950.65112
808.323.179.887.788.971.323.80824
49840.316.026.46012
706.131.024.325.523.420.131.60724
48837.309.460.99012
701.087.133.463.364.331.780.10724
47265.559.939.85012
70.522.081.653.135.618.022.50723
46255.467.159.55712
65.263.469.612.121.696.436.25623
45248.721.045.94712
61.862.158.696.969.685.126.81623
44191.421.191.71612
36.642.072.637.973.627.024.66323
43181.226.428.10412
32.843.018.243.334.281.034.82323
42175.005.213.31412
30.626.824.687.078.642.862.60323
41151.717.587.10512
23.018.226.236.963.262.281.03223
40140.747.479.12212
19.809.852.879.197.825.890.89123
3926.642.122.83011
709.802.708.888.807.208.90721
3817.554.182.21411
308.149.313.202.313.941.80321
3717.471.049.63611
305.237.575.383.575.732.50321
3611.551.134.01811
133.428.697.101.796.824.33121
355.912.650.54410
34.959.436.455.463.495.94320
344.224.722.19210
17.848.277.599.577.284.87120
332.602.899.36310
6.775.085.093.905.805.77619
321.789.471.50410
3.202.208.263.628.022.02319
311.735.796.06410
3.012.987.975.797.892.10319
30152.330.7359
23.204.652.825.640.23217
2991.698.4298
8.408.601.881.068.04816
2890.991.8118
8.279.509.669.059.72816
2783.941.4208
7.046.161.991.616.40716
2626.458.5008
700.052.222.250.00715
2525.654.9578
658.176.818.671.85615
2419.049.0168
362.865.010.568.26315
2318.070.7048
326.550.343.055.62315
225.902.9067
34.844.299.244.84314
214.821.8157
23.249.899.894.23214
202.654.5807
Prime!    7.046.794.976.40713
191.815.5547
3.296.236.326.92313
18823.3636
677.926.629.77612
17190.0346
36.112.921.16311
16180.7046
32.653.935.62311
1515.1955
230.888.0329
1410.5025
110.292.0119
135.6964
32.444.4238
124.8054
23.088.0328
11Prime!    9113
829.9286
102473
61.0165
91183
Prime!    13.9315
8422
1.7714
7Prime!    292
8483
6152
2323
5122
Prime!    1513
491
882
3Prime!    21
Prime!    112
211
81
101
Prime!    71

[SQ8] Case X = 8
One can find the regular numbers of the form n2 + 8 at
%N n^2 + 8. under A189833.
The palindromic numbers of the form n2 + 8 are categorised as follows :
%N n^2 + 8 is a palindrome. under A0?????.
%N Palindromes of the form n^2 + 8. under A0?????.

More terms from Robert Xiao, Nov 11, 2022. See Index Nrs 85 up to 109.
More terms from Robert Xiao, Dec 6, 2022. See Index Nrs 110 up to 124.
More terms from Patrick De Geest, Jun 19, 2023. See Index Nrs 125 up to 129.
More terms from Patrick De Geest, Jul 14, 2023. See Index Nrs 130 up to 136.
1363.138.228.394.911.628.623.233.402.55928
9.848.477.458.629.616.897.259.450.746.470.549.527.986.169.268.547.748.48955
1353.000.000.000.000.000.000.000.000.00128
9.000.000.000.000.000.000.000.000.006.000.000.000.000.000.000.000.000.00955
1341.818.652.420.281.455.671.723.814.45528
3.307.496.625.795.596.477.085.698.755.578.965.807.746.955.975.266.947.03355
1331.818.356.120.335.980.324.208.781.39528
3.306.418.980.363.318.157.562.126.392.936.212.657.518.133.630.898.146.03355
1321.724.202.475.599.784.897.689.740.47228
2.972.874.176.864.426.835.488.286.531.356.828.845.386.244.686.714.782.79255
1311.655.166.102.931.095.240.331.271.44228
2.739.574.828.292.108.963.926.665.829.285.666.293.698.012.928.284.759.37255
130847.924.812.482.000.926.300.298.30327
718.976.487.622.636.433.866.337.481.184.733.668.334.636.226.784.679.81754
129314.100.616.760.138.464.041.582.95927
98.659.197.449.099.376.179.320.598.589.502.397.167.399.094.479.195.68953
128300.000.000.000.000.000.000.000.00127
90.000.000.000.000.000.000.000.000.600.000.000.000.000.000.000.000.00953
127283.771.199.445.191.015.028.966.25027
80.526.093.634.562.377.435.788.584.848.588.753.477.326.543.639.062.50853
126220.273.136.295.247.116.120.061.52427
48.520.254.573.344.512.412.615.068.386.051.621.421.544.337.545.202.58453
125205.649.259.579.543.096.629.767.59627
42.291.617.965.614.298.096.824.407.770.442.869.089.241.656.971.619.22453
12488.261.219.351.619.485.977.009.18726
7.790.042.841.434.690.036.604.736.556.374.066.300.964.341.482.400.97752
12330.495.016.988.938.610.727.189.08926
929.946.061.155.654.492.286.381.595.183.682.294.456.551.160.649.92951
12230.000.000.000.000.000.000.000.00126
900.000.000.000.000.000.000.000.060.000.000.000.000.000.000.000.00951
12120.192.546.102.835.333.965.418.73626
407.738.918.115.130.433.619.266.383.662.916.334.031.511.819.837.70451
12014.758.851.379.769.379.092.268.44826
217.823.694.050.120.504.995.391.848.193.599.405.021.050.496.328.71251
1198.950.092.834.195.860.236.642.99025
80.104.161.740.724.086.156.926.299.262.965.168.042.704.716.140.10850
1185.749.117.659.155.541.635.373.74525
33.052.353.858.814.094.606.298.066.089.260.649.041.885.835.325.03350
1173.000.000.000.000.000.000.000.00125
9.000.000.000.000.000.000.000.006.000.000.000.000.000.000.000.00949
1162.754.287.997.646.479.831.041.20725
7.586.102.373.979.455.287.296.705.076.927.825.549.793.732.016.85749
1151.657.208.480.197.601.900.192.09225
2.746.339.946.838.845.489.363.943.493.639.845.488.386.499.336.47249
114466.760.677.757.715.224.166.55224
217.865.530.300.841.671.584.505.505.485.176.148.003.035.568.71248
113300.000.000.000.000.000.000.00124
90.000.000.000.000.000.000.000.600.000.000.000.000.000.000.00947
112147.534.613.441.008.796.591.05224
21.766.462.163.187.893.463.801.910.836.439.878.136.126.466.71247
11130.000.000.000.000.000.000.00123
900.000.000.000.000.000.000.060.000.000.000.000.000.000.00945
11028.179.624.290.034.425.979.06723
794.091.225.127.498.226.411.848.114.622.894.721.522.190.49745
1093.101.093.480.599.911.050.88122
9.616.780.775.419.270.897.293.927.980.729.145.770.876.16943
1083.000.000.000.000.000.000.00122
9.000.000.000.000.000.000.006.000.000.000.000.000.000.00943
1072.672.192.953.702.229.933.40322
7.140.615.181.815.847.968.343.438.697.485.181.815.160.41743
1062.201.196.652.698.847.497.42622
4.845.266.703.852.610.647.673.767.460.162.583.076.625.48443
1051.823.097.595.796.177.101.36522
3.323.684.843.797.801.143.019.103.411.087.973.484.863.23343
104980.802.221.901.129.592.61921
961.972.998.486.192.653.511.115.356.291.684.899.279.16942
103899.892.100.436.890.609.67021
809.805.792.428.718.816.603.306.618.817.824.297.508.90842
102842.864.975.926.907.854.00321
710.421.367.644.266.956.242.242.659.662.446.763.124.01742
101648.086.163.396.002.532.50421
420.015.675.185.350.092.814.418.290.053.581.576.510.02442
100485.336.002.650.180.553.21821
235.551.035.468.456.064.976.679.460.654.864.530.155.53242
99484.461.473.513.102.602.36821
234.702.919.318.486.614.349.943.416.684.813.919.207.43242
98300.000.000.000.000.000.00121
90.000.000.000.000.000.000.600.000.000.000.000.000.00941
97283.956.551.927.862.350.56021
80.631.323.382.760.787.596.469.578.706.728.332.313.60841
96214.840.990.203.764.785.53421
46.156.651.071.734.156.544.044.565.143.717.015.665.16441
95153.101.038.072.684.534.13221
23.439.927.858.933.599.249.594.299.533.985.872.993.43241
9496.997.592.462.581.797.17920
9.408.532.943.537.105.072.772.705.017.353.492.358.04940
93Prime!    88.059.949.921.538.928.16320
7.754.554.780.183.943.880.330.883.493.810.874.554.57740
9264.004.898.173.356.794.83620
4.096.626.990.181.771.972.222.791.771.810.996.266.90440
9130.764.370.706.994.766.12920
946.446.504.997.397.646.353.646.793.799.405.644.64939
9030.000.000.000.000.000.00120
900.000.000.000.000.000.060.000.000.000.000.000.00939
8928.366.440.488.118.707.58020
804.654.945.965.980.301.151.103.089.569.549.456.40839
8818.225.136.836.285.834.96520
332.155.612.701.342.853.595.358.243.107.216.551.23339
873.104.192.409.439.593.26919
9.636.010.514.822.387.458.547.832.284.150.106.36937
863.069.206.461.297.625.67119
9.420.028.302.071.093.785.873.901.702.038.200.24937
853.000.000.000.000.000.00119
9.000.000.000.000.000.006.000.000.000.000.000.00937
84899.889.741.588.250.33018
809.801.547.015.767.955.559.767.510.745.108.90836
83300.000.000.000.000.00118
90.000.000.000.000.000.600.000.000.000.000.00935
82266.496.356.130.217.00318
71.020.307.830.683.449.594.438.603.870.302.01735
81161.066.420.577.345.21218
25.942.391.837.598.253.135.289.573.819.324.95235
80154.629.361.321.495.61818
23.910.239.382.693.645.054.639.628.393.201.93235
7930.000.000.000.000.00117
900.000.000.000.000.060.000.000.000.000.00933
786.513.071.537.407.80416
42.420.100.851.391.655.619.315.800.102.42432
773.000.000.000.000.00116
9.000.000.000.000.006.000.000.000.000.00931
76576.376.983.170.33515
332.210.426.728.536.635.827.624.012.23330
75481.209.766.450.68215
231.562.839.327.519.915.723.938.265.13230
74300.000.000.000.00115
90.000.000.000.000.600.000.000.000.00929
73275.337.945.056.29315
75.810.983.987.822.222.878.938.901.85729
72216.065.920.101.28415
46.684.481.829.214.441.292.818.448.66429
7194.896.997.097.50114
9.005.440.058.123.113.218.500.445.00928
7046.837.097.362.14814
2.193.713.689.311.331.139.863.173.91228
6930.000.000.000.00114
900.000.000.000.060.000.000.000.00927
6828.285.433.123.40014
800.065.726.978.333.879.627.560.00827
6727.189.036.465.67314
739.243.703.931.696.139.307.342.93727
6622.099.529.046.62614
488.389.184.082.666.280.481.983.88427
6521.644.889.670.81614
468.501.248.861.797.168.842.105.86427
6416.531.889.324.94214
273.303.364.652.131.256.463.303.37227
638.970.276.377.42013
80.465.858.287.299.278.285.856.40826
625.438.671.922.17213
29.579.152.277.022.077.225.197.59226
615.003.245.383.36213
25.032.464.366.133.166.346.423.05226
60Prime!    3.079.298.219.02913
9.482.077.521.715.171.257.702.84925
593.000.000.000.00113
9.000.000.000.006.000.000.000.00925
581.462.512.223.95213
2.138.942.005.209.025.002.498.31225
57313.136.321.25912
98.054.355.691.619.655.345.08923
56300.000.000.00112
90.000.000.000.600.000.000.00923
55275.014.002.59312
75.632.701.622.222.610.723.65723
54Prime!    270.510.768.37312
73.176.075.805.750.857.067.13723
53267.374.937.34712
71.489.357.121.312.175.398.41723
5264.869.123.99611
4.208.003.248.008.423.008.02422
51Prime!    30.000.000.00111
900.000.000.060.000.000.00921
50Prime!    27.157.572.47311
737.533.742.626.247.335.73721
4918.229.113.11511
332.300.564.959.465.003.23321
4816.573.604.59211
274.684.369.171.963.486.47221
479.607.915.38910
92.312.038.122.183.021.32920
465.764.428.66510
33.228.637.833.873.682.23320
454.813.848.68210
23.173.139.133.193.137.13220
443.000.000.00110
9.000.000.006.000.000.00919
432.193.798.27610
4.812.750.875.780.572.18419
421.660.759.75810
2.758.122.973.792.218.57219
41984.531.5319
969.302.335.533.203.96918
40899.936.6709
809.886.010.010.688.90818
39858.762.7239
737.473.414.414.374.73718
38300.000.0019
90.000.000.600.000.00917
37268.086.3039
71.870.265.856.207.81717
36167.274.1589
27.980.643.934.608.97217
35153.532.2829
23.572.161.616.127.53217
34Prime!    30.000.0018
900.000.060.000.00915
3328.370.2808
804.872.787.278.40815
3221.969.6748
482.666.575.666.28415
3114.573.3028
212.381.131.183.21215
303.000.0017
9.000.006.000.00913
292.837.6507
8.052.257.522.50813
282.198.6247
4.833.947.493.38413
272.050.5047
4.204.566.654.02413
26576.2856
332.104.401.23312
25306.9216
94.200.500.24911
24300.0016
90.000.600.00911
23283.6206
80.440.304.40811
22Prime!    96.2115
9.256.556.52910
2185.7735
7.357.007.53710
2030.0015
900.060.0099
1927.5435
758.616.8579
1820.5045
420.414.0249
1718.2355
332.515.2339
16Prime!    8.7074
75.811.8578
156.3644
40.500.5048
14Prime!    3.0014
9.006.0097
132.8404
8.065.6087
129513
904.4096
116543
427.7246
103013
90.6095
92163
46.6645
81723
29.5925
71483
21.9125
6Prime!    312
9693
5272
7373
461
442
3Prime!    51
332
211
91
101
81

[SQ9] Case X = 9
One can find the regular numbers of the form n2 + 9 at
%N n^2 + 9. under A189834.
The palindromic numbers of the form n2 + 9 are categorised as follows :
%N n^2 + 9 is a palindrome. under A0?????.
%N Palindromes of the form n^2 + 9. under A0?????.

More terms from Robert Xiao, Nov 11, 2022. See Index Nrs 58 up to 69.
More terms from Robert Xiao, Dec 6, 2022. See Index Nrs 70 up to 78.
More terms from Patrick De Geest, Jun 19, 2023. See Index Nrs 79 up to 80.
More terms from Patrick De Geest, Jul 14, 2023. See Index Nrs 81 up to 83.
833.000.000.000.000.000.000.000.000.00028
9.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.00955
822.987.683.326.456.987.708.481.160.98328
8.926.251.659.189.091.389.841.064.673.764.601.489.831.909.819.561.526.29855
812.420.121.329.652.660.144.375.022.97628
5.856.987.250.239.759.713.406.390.222.220.936.043.179.579.320.527.896.58555
80300.000.000.000.000.000.000.000.00027
90.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.00953
79187.748.282.862.041.887.561.755.33827
35.249.417.717.645.291.546.629.683.138.692.664.519.254.671.771.494.25353
7830.000.000.000.000.000.000.000.00026
900.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.00951
7718.348.987.163.800.138.442.475.43226
336.685.329.937.302.248.588.849.252.948.885.842.203.739.923.586.63351
763.000.000.000.000.000.000.000.00025
9.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.00949
75300.000.000.000.000.000.000.00024
90.000.000.000.000.000.000.000.000.000.000.000.000.000.000.00947
74241.033.628.665.988.687.276.72624
58.097.210.147.893.723.446.074.347.064.432.739.874.101.279.08547
73225.629.438.726.311.944.830.66424
50.908.643.619.950.556.377.188.488.177.365.505.991.634.680.90547
72223.784.616.483.317.675.634.38624
50.079.554.574.585.577.129.303.230.392.177.558.547.545.597.00547
7130.000.000.000.000.000.000.00023
900.000.000.000.000.000.000.000.000.000.000.000.000.000.00945
7022.996.261.020.893.993.983.60423
528.828.020.941.088.478.395.333.593.874.880.149.020.828.82545
693.000.000.000.000.000.000.00022
9.000.000.000.000.000.000.000.000.000.000.000.000.000.00943
682.854.381.712.129.441.577.09722
8.147.494.958.539.002.284.892.984.822.009.358.594.947.41843
671.827.952.173.486.822.966.13222
3.341.409.148.555.200.126.851.586.210.025.558.419.041.43343
66300.308.020.167.822.829.41021
90.184.906.977.117.483.249.994.238.471.177.960.948.10941
65300.000.000.000.000.000.00021
90.000.000.000.000.000.000.000.000.000.000.000.000.00941
64228.626.626.561.466.931.59621
52.270.134.372.876.456.677.977.665.467.827.343.107.22541
63228.039.420.495.316.042.49621
52.001.977.299.839.566.340.304.366.593.899.277.910.02541
6230.000.000.000.000.000.00020
900.000.000.000.000.000.000.000.000.000.000.000.00939
613.000.000.000.000.000.00019
9.000.000.000.000.000.000.000.000.000.000.000.00937
602.420.491.660.367.448.52419
5.858.779.877.908.367.775.777.638.097.789.778.58537
592.386.963.601.801.232.36619
5.697.595.236.323.912.188.812.193.236.325.957.96537
581.983.109.734.536.126.12819
3.932.724.219.211.944.642.464.491.129.124.272.39337
57300.015.673.824.225.70018
90.009.404.540.204.185.858.140.204.540.490.00935
56300.000.000.000.000.00018
90.000.000.000.000.000.000.000.000.000.000.00935
5530.074.841.278.007.12017
904.496.077.897.320.939.023.798.770.694.40933
5430.000.000.000.000.00017
900.000.000.000.000.000.000.000.000.000.00933
5324.213.184.844.776.47417
586.278.320.327.313.121.313.723.023.872.68533
5223.809.076.639.223.78417
566.872.130.412.431.717.134.214.031.278.66533
5123.724.561.255.743.48417
562.854.806.777.524.838.425.777.608.458.26533
5020.752.370.363.370.60517
430.660.875.698.502.616.205.896.578.066.03433
493.000.000.000.000.00016
9.000.000.000.000.000.000.000.000.000.00931
482.338.836.516.042.64416
5.470.156.248.774.492.944.778.426.510.74531
472.079.319.170.475.63516
4.323.568.212.707.482.847.072.128.653.23431
461.985.156.016.920.02216
3.940.844.411.513.766.673.151.144.480.49331
45300.000.000.000.00015
90.000.000.000.000.000.000.000.000.00929
44Prime!    299.142.331.546.06715
89.486.134.522.817.071.822.543.168.49829
43241.848.269.901.92615
58.490.585.654.554.845.545.658.509.48529
42233.022.488.525.89415
54.299.480.158.800.400.885.108.499.24529
4130.000.000.000.00014
900.000.000.000.000.000.000.000.00927
403.000.020.251.10013
9.000.121.507.010.107.051.210.00925
393.000.000.000.00013
9.000.000.000.000.000.000.000.00925
382.983.356.089.71713
8.900.413.558.051.508.553.140.09825
37301.053.306.56012
90.633.093.390.709.339.033.60923
36300.804.083.72012
90.483.096.782.628.769.038.40923
35300.000.000.00012
90.000.000.000.000.000.000.00923
34291.644.222.50712
85.056.352.521.712.525.365.05823
33288.652.169.57312
83.320.074.999.199.947.002.33823
32285.771.472.35312
81.665.334.410.801.443.356.61823
31193.566.472.90812
37.467.979.434.043.497.976.47323
30189.532.984.71212
35.922.752.293.839.225.722.95323
2930.000.000.00011
900.000.000.000.000.000.00921
283.000.000.00010
9.000.000.000.000.000.00919
271.836.534.08210
3.372.857.434.347.582.73319
26301.021.9609
Prime!    90.614.220.402.241.60917
25300.000.0009
90.000.000.000.000.00917
24292.676.6579
85.659.625.552.695.65817
23198.306.1289
39.325.320.402.352.39317
2230.000.0008
900.000.000.000.00915
2119.282.1428
371.801.000.108.17315
203.000.0007
9.000.000.000.00913
19Prime!    2.987.9837
8.928.042.408.29813
182.854.0977
8.145.869.685.41813
171.892.0887
3.579.996.999.75313
16300.0006
90.000.000.00911
15234.0946
54.800.000.84511
14230.0546
52.924.842.92511
1330.0005
900.000.0099
1223.8665
569.585.9659
1119.2925
372.181.2739
103.0004
9.000.0097
92.4244
5.875.7857
83003
90.0095
7Prime!    2933
85.8585
61883
Prime!    35.3535
51823
33.1335
4302
9093
3242
5853
2182
3333
101
91
```

```

Contributions

[ November 4, 2022 ]
Robert Xiao (email) added a missing entry for Case X = 2 [n^2 + 2] or SQ2 [40].

[ November 11, 2022 ]
for Case X = 2 [n^2 + 2] entries [91] up to [111].
for Case X = 3 [n^2 + 3] entries [66] up to [77].
for Case X = 4 [n^2 + 4] entries [87] up to [121].
for Case X = 5 [n^2 + 5] entries [58] up to [65].
for Case X = 6 [n^2 + 6] entries [61] up to [82].
for Case X = 7 [n^2 + 7] entries [81] up to [96].
for Case X = 8 [n^2 + 8] entries [85] up to [109].
for Case X = 9 [n^2 + 9] entries [58] up to [69].

[ December 6, 2022 ]
for Case X = 2 [n^2 + 2] entries [112] up to [127].
for Case X = 3 [n^2 + 3] entries [78] up to [91].
for Case X = 4 [n^2 + 4] entries [122] up to [164].
for Case X = 5 [n^2 + 5] entries [66] up to [76].
for Case X = 6 [n^2 + 6] entries [83] up to [97].
for Case X = 7 [n^2 + 7] entries [97] up to [126].
for Case X = 8 [n^2 + 8] entries [110] up to [124].
for Case X = 9 [n^2 + 9] entries [70] up to [78].

[ June 19, 2023 ]
for Case X = 2 [n^2 + 2] entries [128] up to [129].
for Case X = 3 [n^2 + 3] entries [92] up to [94].
for Case X = 4 [n^2 + 4] entries [165] up to [174].
for Case X = 5 [n^2 + 5] entries [77] up to [80].
for Case X = 6 [n^2 + 6] entries [98] up to [100].
for Case X = 7 [n^2 + 7] entry [127].
for Case X = 8 [n^2 + 8] entries [125] up to [129].
for Case X = 9 [n^2 + 9] entries [79] up to [80].

[ July 14, 2023 ]
for Case X = 2 [n^2 + 2] entries [130] up to [132].
for Case X = 3 [n^2 + 3] entry [95].
for Case X = 4 [n^2 + 4] entries [175] up to [188].
for Case X = 5 [n^2 + 5] entries [81] up to [84].
for Case X = 6 [n^2 + 6] entry [101].
for Case X = 7 [n^2 + 7] entries [128] up to [130].
for Case X = 8 [n^2 + 8] entries [130] up to [136].
for Case X = 9 [n^2 + 9] entries [81] up to [83].

```

```