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Palindromic Incremented Squares
of the form n^2+X
rood n^2+0 rood n^2+1 rood n^2+(n+1) rood comments



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

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

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

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
9 can only be followed by 2 : 92

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

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

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

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

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


An infinite palindromic pattern resides 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 hides 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 Nr BasenumberLength
Palindromic Incremented Squares of form n^2+XLength
up down
Case X = 0
See in-depth webpage about Palindromic Square Numbers
up down
Case X = 1
See in-depth webpage about Palindromic Incremented Squares
up down
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 A0?????.
%N Palindromes of the form n^2 + 2. under A0?????.
68817.683.802.207.30815
668.606.800.392.199.991.293.008.606.86630
67791.470.648.804.93215
626.425.787.919.700.007.919.787.524.62630
66364.768.101.292.42715
133.055.767.720.482.284.027.767.550.33130
65284.676.297.563.00415
81.040.594.394.179.997.149.349.504.01829
64186.797.158.329.47115
34.893.178.359.965.456.995.387.139.84329
63141.426.468.677.10015
20.001.446.042.474.747.424.064.410.00229
62140.737.100.319.08315
19.806.931.406.223.632.260.413.960.89129
61133.805.135.860.43715
17.903.814.382.630.003.628.341.830.97129
6093.455.496.826.37614
8.733.929.887.064.774.607.889.293.37828
5955.349.225.724.44914
3.063.536.788.296.006.928.876.353.60328
5845.492.981.517.64014
2.069.611.367.364.334.637.631.169.60228
5714.363.881.876.06014
206.321.102.549.404.945.201.123.60227
5613.413.161.997.31314
179.912.914.766.161.667.419.219.97127
5510.902.121.823.94714
118.856.260.264.181.462.062.658.81127
549.114.951.055.99413
83.082.332.753.166.135.723.328.03826
542.925.054.461.66613
8.555.943.603.712.173.063.495.55825
532.688.021.576.51513
7.225.459.995.810.185.999.545.22725
521.954.611.231.09113
3.820.505.064.707.074.605.050.28325
511.861.509.029.37913
3.465.215.866.459.546.685.125.64325
50268.803.849.76512
72.255.509.648.484.690.555.22723
49250.793.696.73212
62.897.478.320.502.387.479.82623
48144.598.910.53012
20.908.844.926.462.944.880.90223
47142.019.320.31012
20.169.487.341.314.378.496.10223
4611.645.196.02311
135.610.590.414.095.016.53121
458.487.412.69510
72.036.174.255.247.163.02720
448.486.324.85510
72.017.709.544.590.771.02720
433.881.830.25710
15.068.606.144.160.686.05120
422.496.801.51810
6.234.017.820.287.104.32619
411.950.914.24110
3.806.066.375.736.606.08319
401.912.253.83110
3.656.714.714.174.176.56319
391.340.374.43710
1.796.603.631.363.066.97119
38813.448.3589
661.698.231.132.896.16618
37620.208.5599
384.658.656.656.856.48318
36452.357.9209
204.627.687.786.726.40218
35451.977.3209
204.283.497.794.382.40218
34246.553.4489
60.788.602.720.688.70617
33186.062.6299
34.619.301.910.391.64317
3279.094.2828
6.255.905.445.095.52616
3161.875.0918
3.828.526.886.258.28316
3028.559.2548
815.630.989.036.51815
2926.237.6228
688.412.808.214.88615
2825.809.8928
666.150.525.051.66615
2714.365.9408
206.380.232.083.60215
265.513.9517
30.403.655.630.40314
252.491.0327
6.205.240.425.02613
241.845.5717
3.406.132.316.04313
231.050.5037
1.103.556.553.01113
22902.6966
814.860.068.41812
21423.4376
179.298.892.97112
20298.4366
89.064.046.09811
19268.8656
72.288.388.22711
18140.8336
19.833.933.89111
1710.5035
110.313.0119
164.5404
20.611.6028
153.6274
13.155.1318
142.9864
8.916.1987
132.9164
8.503.0587
122.5384
6.441.4467
111.8114
3.279.7237
108283
685.5866
93932
154.4516
82582
66.5665
7852
7.2274
6192
3633
5132
1713
481
662
331
112
221
61
111
31
001
21
up down
Case X = 3
One can find the regular numbers of the form n2 + 3 at
%N n^2 + 3. under A0?????.
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?????.
51211.877.852.724.47115
44.892.224.475.132.623.157.442.229.84429
50200.000.000.000.00115
40.000.000.000.000.400.000.000.000.00429
49159.657.521.992.89315
25.490.524.328.911.111.982.342.509.45229
48145.112.248.387.50315
21.057.564.632.076.367.023.646.575.01229
4727.276.194.939.18814
743.990.810.360.585.063.018.099.34727
4620.000.000.000.00114
400.000.000.000.040.000.000.000.00427
452.201.668.436.94113
4.847.343.906.222.226.093.437.48425
442.006.428.407.60113
4.025.754.954.828.284.594.575.20425
432.000.000.000.00113
4.000.000.000.004.000.000.000.00425
42312.477.762.97412
97.642.352.353.235.325.324.67923
41200.000.000.00112
40.000.000.000.400.000.000.00423
40175.791.724.53012
30.902.730.413.231.403.720.90323
39170.460.122.78312
29.056.653.459.195.435.665.09223
38160.164.390.40712
25.652.631.954.445.913.625.65223
3720.000.000.00111
400.000.000.040.000.000.00421
3617.038.650.78311
290.315.620.505.026.513.09221
352.196.849.65910
4.826.148.424.248.416.28419
342.020.653.09910
4.083.038.946.498.303.80419
332.011.953.70110
4.047.957.694.967.597.40419
332.000.000.00110
4.000.000.004.000.000.00419
321.750.740.84010
3.065.093.488.843.905.60319
311.745.447.58010
3.046.587.254.527.856.40319
301.582.907.50710
2.505.596.175.716.955.05219
29287.490.3259
82.650.686.968.605.62817
28276.529.5929
76.468.615.251.686.46717
27201.146.4519
40.459.894.749.895.40417
26200.000.0019
40.000.000.400.000.00417
25174.546.0809
30.466.334.043.366.40317
2420.104.2998
404.182.838.281.40415
2320.000.0018
400.000.040.000.00415
222.808.6227
7.888.357.538.88713
212.211.1097
4.889.003.009.88413
202.000.0017
4.000.004.000.00413
19200.0016
40.000.400.00411
18167.3136
27.993.639.97211
17165.8376
27.501.910.57211
16152.1276
23.142.624.13211
15145.7976
21.256.765.21211
1431.6145
999.444.9999
1330.5065
930.616.0399
1221.1295
446.434.6449
1120.0015
400.040.0049
102.8754
8.265.6287
92.0014
4.004.0047
83063
93.6395
72013
40.4045
61473
21.6125
5282
7873
4212
4443
3172
2923
221
71
111
41
001
31
up down
Case X = 4
One can find the regular numbers of the form n2 + 4 at
%N n^2 + 4. under A0?????.
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?????.
64290.001.098.900.01215
84.100.637.363.214.541.236.373.600.14829
63290.000.000.000.01215
84.100.000.000.006.960.000.000.000.14829
62225.116.991.118.80115
50.677.659.690.382.328.309.695.677.60529
61200.000.000.000.00015
40.000.000.000.000.000.000.000.000.00429
6029.001.099.890.01214
841.063.794.830.454.038.497.360.14827
5929.001.089.109.98814
841.063.169.565.464.565.961.360.14827
5829.000.108.900.01214
841.006.316.212.555.212.613.600.14827
5729.000.010.999.98814
841.000.637.999.424.999.736.000.14827
5629.000.000.000.01214
841.000.000.000.696.000.000.000.14827
5524.096.294.452.00914
580.631.406.317.919.713.604.136.08527
5423.283.121.322.42114
542.103.738.514.575.415.837.301.24527
5320.102.019.998.52014
404.091.208.020.898.020.802.190.40427
5220.000.000.000.00014
400.000.000.000.000.000.000.000.00427
5117.784.936.509.39714
316.303.966.643.282.346.669.303.61327
502.900.109.890.01213
8.410.637.374.145.414.737.360.14825
492.900.000.000.01213
8.410.000.000.069.600.000.000.14825
482.000.000.000.00013
4.000.000.000.000.000.000.000.00425
471.893.180.648.20713
3.584.132.966.745.476.692.314.85325
46291.098.901.08812
84.738.570.214.641.207.583.74823
45290.010.890.01212
84.106.316.325.552.361.360.14823
44290.001.099.98812
84.100.637.994.249.973.600.14823
43290.000.000.01212
84.100.000.006.960.000.000.14823
42234.304.304.47112
54.898.507.093.639.070.589.84523
41200.000.000.00012
40.000.000.000.000.000.000.00423
4029.010.989.01211
841.637.483.454.384.736.14821
3929.000.000.01211
841.000.000.696.000.000.14821
3820.046.487.91011
401.861.677.525.776.168.10421
3720.000.000.00011
400.000.000.000.000.000.00421
362.901.089.01210
8.416.317.455.547.136.14819
352.900.109.98810
8.410.637.942.497.360.14819
342.900.000.01210
8.410.000.069.600.000.14819
332.418.272.55910
5.848.042.169.612.408.48519
322.000.000.00010
4.000.000.000.000.000.00419
311.981.904.48310
3.927.945.379.735.497.29319
30293.695.2929
86.256.924.542.965.26817
29291.098.9129
84.738.576.567.583.74817
28290.000.0129
84.100.006.960.000.14817
27200.000.0009
40.000.000.000.000.00417
26197.605.7179
39.048.019.391.084.09317
25177.437.6539
31.484.120.702.148.41317
2429.108.9128
847.328.757.823.74815
2329.010.9888
841.637.424.736.14815
2229.000.0128
841.000.696.000.14815
2124.208.2918
586.041.353.140.68515
2023.020.9118
529.962.343.269.92515
1920.000.0008
400.000.000.000.00415
182.900.0127
8.410.069.600.14813
172.000.0007
4.000.000.000.00413
16291.0886
84.732.223.74811
15290.0126
84.106.960.14811
14284.2986
80.825.352.80811
13200.0006
40.000.000.00411
1229.0125
841.696.1489
1120.2305
409.252.9049
1020.0005
400.000.0049
92.9124
8.479.7487
82.3694
5.612.1657
72.3294
5.424.2457
62.0004
4.000.0047
52413
58.0855
42003
40.0045
3202
4043
221
81
111
51
001
41
up down
Case X = 5
One can find the regular numbers of the form n2 + 5 at
%N n^2 + 5. under A0?????.
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?????.
43309.910.900.890.99215
96.044.766.491.066.266.019.466.744.06929
42262.407.097.891.85915
68.857.485.024.027.672.042.058.475.88629
41204.099.968.332.39715
41.656.797.073.285.458.237.079.765.61429
40120.984.198.909.69415
14.637.176.385.820.402.858.367.173.64129
39120.357.148.031.79415
14.485.843.082.347.174.328.034.858.44129
38112.770.894.443.84615
12.717.274.633.665.056.633.647.271.72129
3731.090.089.099.10814
966.593.640.190.474.091.046.395.66927
3630.990.990.990.99214
960.441.522.603.747.306.225.144.06927
3525.763.006.263.48114
663.732.491.732.161.237.194.237.36627
3412.686.342.618.41614
160.943.289.031.838.130.982.349.06127
333.048.771.427.88213
9.295.007.219.469.649.127.005.92925
322.256.574.603.77013
5.092.128.942.379.732.498.212.90525
31309.910.890.99212
96.044.760.355.455.306.744.06923
30225.101.642.74012
50.670.749.564.246.594.707.60523
29218.488.832.63712
47.737.369.987.078.996.373.77423
28214.091.717.95712
45.835.263.697.779.636.253.85423
2730.990.990.99211
960.441.522.666.225.144.06921
2622.360.694.00011
500.000.636.161.636.000.00521
2512.996.564.68411
168.910.693.585.396.019.86121
243.108.910.89210
9.665.326.934.396.235.66919
233.099.109.00810
9.604.476.643.466.744.06919
223.049.566.11810
9.299.853.508.053.589.92919
212.172.438.48710
4.719.488.979.798.849.17419
202.171.728.98710
4.716.406.792.976.046.17419
19310.900.8929
96.659.364.646.395.66917
18307.606.2629
94.621.612.421.612.64917
17204.050.6039
41.636.648.584.663.61417
16203.480.3479
41.404.251.615.240.41417
1531.089.1088
966.532.636.235.66915
1430.990.9928
960.441.585.144.06915
1324.619.1998
606.104.959.401.60615
1220.920.2778
437.657.989.756.73415
1113.778.3248
189.842.212.248.98115
101.007.4367
1.014.927.294.10113
9310.8926
96.653.835.66911
8136.4746
18.625.152.68111
722.5705
509.404.9059
620.3475
414.000.4149
51.3744
1.887.8817
41.0144
1.028.2017
32033
41.2145
221
91
111
61
001
51
up down
Case X = 6
One can find the regular numbers of the form n2 + 6 at
%N n^2 + 6. under A0?????.
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?????.
45455.835.912.156.23615
207.786.378.811.307.703.118.873.687.70230
44114.028.867.547.99515
13.002.582.634.278.187.243.628.520.03129
4327.668.521.984.58114
765.547.108.811.242.118.801.745.56727
421.622.457.383.43413
2.632.367.961.059.501.697.632.36225
41360.616.362.24512
130.044.160.718.817.061.440.03124
40234.732.340.24312
55.099.271.555.955.517.299.05523
39162.829.334.66612
26.513.392.227.772.229.331.56223
38157.495.523.40612
24.804.839.892.929.893.840.84223
37157.302.301.85612
24.744.014.169.196.141.044.74223
36144.260.002.21412
20.810.948.238.783.284.901.80223
3536.131.148.25511
1.305.459.874.224.789.545.03122
3428.043.323.45911
786.427.990.626.099.724.68721
3327.979.618.65911
782.859.060.303.060.958.28721
323.645.161.86510
13.287.205.022.050.278.23120
312.354.704.14310
5.544.631.601.061.364.45519
301.554.076.05610
2.415.152.387.832.515.14219
29360.581.0059
130.018.661.166.810.03118
28156.832.7449
24.596.509.590.569.54217
27144.402.2869
20.852.020.202.025.80217
2688.574.6918
7.845.475.885.745.48716
2524.589.4208
604.639.575.936.40615
2423.954.0378
573.795.888.597.37515
2316.963.9248
287.774.717.477.78215
2211.504.3658
132.350.414.053.23115
2111.493.7158
132.105.484.501.23115
208.493.4897
72.139.355.393.12714
197.586.6637
57.557.455.475.57514
18245.8206
60.427.472.40611
17230.6236
53.186.968.13511
16169.8746
28.857.175.88211
15144.6646
20.927.672.90211
1486.3795
7.461.331.64710
1316.7765
281.434.1829
1215.5565
241.989.1429
1111.5155
132.595.2319
102.7294
7.447.4477
91563
24.3425
81153
13.2315
7732
5.3354
6232
5353
5162
2623
4142
2023
371
552
241
222
111
71
001
61
up down
Case X = 7
One can find the regular numbers of the form n2 + 7 at
%N n^2 + 7. under A0?????.
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?????.
63928.397.928.617.61915
861.922.713.861.485.584.168.317.229.16830
62894.779.501.236.75115
800.630.355.833.488.884.338.553.036.00830
61390.478.814.572.83815
152.473.704.630.208.802.036.407.374.25130
60247.007.970.190.24715
61.012.937.337.505.950.573.373.921.01629
59139.767.782.028.82815
19.535.032.893.257.975.239.823.053.59129
58124.845.622.180.88815
15.586.429.377.733.033.777.392.468.55129
5726.346.484.384.43314
694.137.239.419.171.914.932.731.49627
5615.258.510.823.13514
232.822.152.539.727.935.251.228.23227
5511.545.204.077.98214
133.291.737.202.252.202.737.192.33127
548.372.856.137.01013
70.104.719.891.066.019.891.740.10726
538.356.234.672.33313
69.826.657.899.100.199.875.662.89626
528.309.775.585.96713
69.052.370.289.133.198.207.325.09626
513.693.414.147.56813
13.641.308.065.455.456.080.314.63126
501.065.362.822.95213
1.134.997.944.528.254.497.994.31125
49921.146.111.27912
848.510.158.324.423.851.015.84824
48899.067.950.65112
808.323.179.887.788.971.323.80824
47840.316.026.46012
706.131.024.325.523.420.131.60724
46837.309.460.99012
701.087.133.463.364.331.780.10724
45265.559.939.85012
70.522.081.653.135.618.022.50723
44255.467.159.55712
65.263.469.612.121.696.436.25623
43248.721.045.94712
61.862.158.696.969.685.126.81623
42191.421.191.71612
36.642.072.637.973.627.024.66323
41181.226.428.10412
32.843.018.243.334.281.034.82323
40175.005.213.31412
30.626.824.687.078.642.862.60323
39151.717.587.10512
23.018.226.236.963.262.281.03223
38140.747.479.12212
19.809.852.879.197.825.890.89123
3726.642.122.83011
709.802.708.888.807.208.90721
3617.554.182.21411
308.149.313.202.313.941.80321
3517.471.049.63611
305.237.575.383.575.732.50321
3411.551.134.01811
133.428.697.101.796.824.33121
335.912.650.54410
34.959.436.455.463.495.94320
324.224.722.19210
17.848.277.599.577.284.87120
312.602.899.36310
6.775.085.093.905.805.77619
301.789.471.50410
3.202.208.263.628.022.02319
291.735.796.06410
3.012.987.975.797.892.10319
28152.330.7359
23.204.652.825.640.23217
2791.698.4298
8.408.601.881.068.04816
2690.991.8118
8.279.509.669.059.72816
2583.941.4208
7.046.161.991.616.40716
2426.458.5008
700.052.222.250.00715
2325.654.9578
658.176.818.671.85615
2219.049.0168
362.865.010.568.26315
2118.070.7048
326.550.343.055.62315
205.902.9067
34.844.299.244.84314
194.821.8157
23.249.899.894.23214
182.654.5807
7.046.794.976.40713
171.815.5547
3.296.236.326.92313
16823.3636
677.926.629.77612
15190.0346
36.112.921.16311
14180.7046
32.653.935.62311
1315.1955
230.888.0329
1210.5025
110.292.0119
115.6964
32.444.4238
104.8054
23.088.0328
99113
829.9286
82473
61.0165
71183
13.9315
6422
1.7714
5292
8483
5152
2323
4122
1513
391
882
221
112
111
81
001
71
up down
Case X = 8
One can find the regular numbers of the form n2 + 8 at
%N n^2 + 8. under A0?????.
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?????.
75576.376.983.170.33515
332.210.426.728.536.635.827.624.012.23330
74481.209.766.450.68215
231.562.839.327.519.915.723.938.265.13230
73300.000.000.000.00115
90.000.000.000.000.600.000.000.000.00929
72275.337.945.056.29315
75.810.983.987.822.222.878.938.901.85729
71216.065.920.101.28415
46.684.481.829.214.441.292.818.448.66429
7094.896.997.097.50114
9.005.440.058.123.113.218.500.445.00928
6946.837.097.362.14814
2.193.713.689.311.331.139.863.173.91228
6830.000.000.000.00114
900.000.000.000.060.000.000.000.00927
6728.285.433.123.40014
800.065.726.978.333.879.627.560.00827
6627.189.036.465.67314
739.243.703.931.696.139.307.342.93727
6522.099.529.046.62614
488.389.184.082.666.280.481.983.88427
6421.644.889.670.81614
468.501.248.861.797.168.842.105.86427
6316.531.889.324.94214
273.303.364.652.131.256.463.303.37227
628.970.276.377.42013
80.465.858.287.299.278.285.856.40826
615.438.671.922.17213
29.579.152.277.022.077.225.197.59226
605.003.245.383.36213
25.032.464.366.133.166.346.423.05226
593.079.298.219.02913
9.482.077.521.715.171.257.702.84925
583.000.000.000.00113
9.000.000.000.006.000.000.000.00925
571.462.512.223.95213
2.138.942.005.209.025.002.498.31225
56313.136.321.25912
98.054.355.691.619.655.345.08923
55300.000.000.00112
90.000.000.000.600.000.000.00923
54275.014.002.59312
75.632.701.622.222.610.723.65723
53270.510.768.37312
73.176.075.805.750.857.067.13723
52267.374.937.34712
71.489.357.121.312.175.398.41723
5164.869.123.99611
4.208.003.248.008.423.008.02422
5030.000.000.00111
900.000.000.060.000.000.00921
4927.157.572.47311
737.533.742.626.247.335.73721
4818.229.113.11511
332.300.564.959.465.003.23321
4716.573.604.59211
274.684.369.171.963.486.47221
469.607.915.38910
92.312.038.122.183.021.32920
455.764.428.66510
33.228.637.833.873.682.23320
444.813.848.68210
23.173.139.133.193.137.13220
433.000.000.00110
9.000.000.006.000.000.00919
422.193.798.27610
4.812.750.875.780.572.18419
411.660.759.75810
2.758.122.973.792.218.57219
40984.531.5319
969.302.335.533.203.96918
39899.936.6709
809.886.010.010.688.90818
38858.762.7239
737.473.414.414.374.73718
37300.000.0019
90.000.000.600.000.00917
36268.086.3039
71.870.265.856.207.81717
35167.274.1589
27.980.643.934.608.97217
34153.532.2829
23.572.161.616.127.53217
3330.000.0018
900.000.060.000.00915
3228.370.2808
804.872.787.278.40815
3121.969.6748
482.666.575.666.28415
3014.573.3028
212.381.131.183.21215
293.000.0017
9.000.006.000.00913
282.837.6507
8.052.257.522.50813
272.198.6247
4.833.947.493.38413
262.050.5047
4.204.566.654.02413
25576.2856
332.104.401.23312
24306.9216
94.200.500.24911
23300.0016
90.000.600.00911
22283.6206
80.440.304.40811
2196.2115
9.256.556.52910
2085.7735
7.357.007.53710
1930.0015
900.060.0099
1827.5435
758.616.8579
1720.5045
420.414.0249
1618.2355
332.515.2339
158.7074
75.811.8578
146.3644
40.500.5048
133.0014
9.006.0097
122.8404
8.065.6087
119513
904.4096
106543
427.7246
93013
90.6095
82163
46.6645
71723
29.5925
61483
21.9125
5312
9693
4272
7373
361
442
251
332
111
91
001
81
up down
Case X = 9
One can find the regular numbers of the form n2 + 9 at
%N n^2 + 9. under A0?????.
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?????.
44300.000.000.000.00015
90.000.000.000.000.000.000.000.000.00929
43299.142.331.546.06715
89.486.134.522.817.071.822.543.168.49829
42241.848.269.901.92615
58.490.585.654.554.845.545.658.509.48529
41233.022.488.525.89415
54.299.480.158.800.400.885.108.499.24529
4030.000.000.000.00014
900.000.000.000.000.000.000.000.00927
393.000.020.251.10013
9.000.121.507.010.107.051.210.00925
383.000.000.000.00013
9.000.000.000.000.000.000.000.00925
372.983.356.089.71713
8.900.413.558.051.508.553.140.09825
36301.053.306.56012
90.633.093.390.709.339.033.60923
35300.804.083.72012
90.483.096.782.628.769.038.40923
34300.000.000.00012
90.000.000.000.000.000.000.00923
33291.644.222.50712
85.056.352.521.712.525.365.05823
32288.652.169.57312
83.320.074.999.199.947.002.33823
31285.771.472.35312
81.665.334.410.801.443.356.61823
30193.566.472.90812
37.467.979.434.043.497.976.47323
29189.532.984.71212
35.922.752.293.839.225.722.95323
2830.000.000.00011
900.000.000.000.000.000.00921
273.000.000.00010
9.000.000.000.000.000.00919
261.836.534.08210
3.372.857.434.347.582.73319
25301.021.9609
90.614.220.402.241.60917
24300.000.0009
90.000.000.000.000.00917
23292.676.6579
85.659.625.552.695.65817
22198.306.1289
39.325.320.402.352.39317
2130.000.0008
900.000.000.000.00915
2019.282.1428
371.801.000.108.17315
193.000.0007
9.000.000.000.00913
182.987.9837
8.928.042.408.29813
172.854.0977
8.145.869.685.41813
161.892.0887
3.579.996.999.75313
15300.0006
90.000.000.00911
14234.0946
54.800.000.84511
13230.0546
52.924.842.92511
1230.0005
900.000.0099
1123.8665
569.585.9659
1019.2925
372.181.2739
93.0004
9.000.0097
82.4244
5.875.7857
73003
90.0095
62933
85.8585
51883
35.3535
41823
33.1335
3302
9093
2242
5853
1182
3333
001
91




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