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Subsets of Palindromic Squares
rood Squares upto length 31 rood Squares from length 32
rood Palindromic Squares rood Factorization rood comments


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Sources Revealed


Neil Sloane's "Integer Sequences" Encyclopedia can be consulted online :
Neil Sloane's Integer Sequences
The subsets of palindromic squares are categorised as follows :
separator
%N n^2 is a palindromic square of sporadic type. under A059744.
%N Palindromic squares of sporadic type. under A059745.
separator
%N Square is a palindrome with even number of digits. under A016113.
%N Palindromic squares with an even number of digits. under A027829.
separator
%N Square is a palindrome with odd number of digits. under A028816.
%N Palindromic squares with odd number of digits. under A028817.
separator
%N Nonpalindromic & "non-core" numbers that when squared give palindromes
with odd number of digits. under A016106.
%N Palindromic squares with odd number of digits and nonpalindromic & "non-core"
square roots. under A028818.
%N Asymmetric families of palindromic squares. under A007573.
separator
Click here to view some of the author's [P. De Geest] entries to the table.
Click here to view some entries to the table about palindromes.






Sporadic Palindromic Squares of EVEN length
[TOP OF PAGE] [SUBSET B] [SUBSET C]
          
rood Full Listing


Serial
Number
Index BasenumberLength
Palindromic Square NumberLength
   
See also Sloane's A059744 and A059745
18 p7 64.897.400.105.515.621.177.314.68226
4.211.672.540.455.378.958.718.869.999.688.178.598.735.540.452.761.12452
17 p6 4.275.548.277.509.699.161.443.65925
18.280.313.073.316.155.472.257.355.375.227.455.161.337.031.308.28150
16 p3 831.775.153.121.251.039.203.51424
691.849.905.349.880.612.384.525.525.483.216.088.943.509.948.19648
15 p2 722.956.456.358.957.313.434.53524
522.666.037.791.100.950.480.675.576.084.059.001.197.730.666.22548
14 1555 3.823.177.109.095.314.778.62122
14.616.683.207.510.408.440.555.504.480.401.570.238.661.64144
13 1373 637.323.988.797.048.057.09821
406.181.866.696.179.837.389.983.738.971.696.668.181.60442
12 740 795.559.265.009.384.10618
632.914.544.142.271.449.944.172.241.445.419.23636
11 739 633.856.150.760.638.65218
401.773.619.857.093.475.574.390.758.916.377.10436
10 738 404.099.764.753.665.98118
163.296.619.873.968.186.681.869.378.916.692.36136
9 639 40.447.213.778.058.76917
1.635.977.102.407.987.117.897.042.017.795.36134
8 485 6.819.209.882.215.74216
46.501.623.417.708.833.880.771.432.610.56432
7 309 98.275.825.201.58714
9.658.137.819.052.882.509.187.318.56928
6 308 69.800.670.077.02814
4.872.133.543.202.112.023.453.312.78428
5 263 6.360.832.925.89813
40.460.195.511.188.111.559.106.40426
4 161 83.163.115.48611
6.916.103.777.337.773.016.19622
3 69 64.030.6488
4.099.923.883.299.90416
2 36 798.6446
637.832.238.73612
1 14 8363
698.8966


Sporadic Palindromic Squares of ODD length
[TOP OF PAGE] [SUBSET C] [SUBSET A]
          
rood Full Listing


Serial
Number
Index BasenumberLength
Palindromic Square NumberLength
   
See also Sloane's A059744 and A059745
76 p13 1.373.512.530.649.258.635.292.477.60928
1.886.536.671.850.530.641.991.373.196.913.731.991.460.350.581.766.356.88155
75 p12 1.208.997.217.707.381.836.451.672.37128
1.461.674.272.424.190.432.753.231.165.611.323.572.340.914.242.724.761.64155
74 p11 1.103.866.360.472.916.946.437.760.98928
1.218.520.941.783.723.816.716.782.817.182.876.176.183.273.871.490.258.12155
73 p10 219.293.240.651.172.832.756.867.92227
48.089.525.395.293.201.014.489.455.855.498.441.010.239.259.352.598.08453
72 p9 122.063.831.551.139.898.460.740.72127
14.899.578.972.945.056.149.893.218.681.239.894.165.054.927.987.599.84153
71 p8 121.096.650.591.136.334.960.853.87927
14.664.398.784.391.760.063.516.738.283.761.536.006.719.348.789.346.64153
70 p5 2.198.834.453.254.769.178.871.87225
4.834.872.952.820.199.705.196.890.986.915.079.910.282.592.784.38449
69 p4 2.107.561.207.005.423.534.632.46225
4.441.814.241.274.157.711.392.425.242.931.177.514.721.424.181.44449
68 p1 136.569.391.518.194.940.977.04124
18.651.198.699.650.016.285.556.865.558.261.005.699.689.115.68147
67 1939 25.886.574.803.023.261.617.72623
670.114.755.032.518.816.023.606.320.618.815.230.557.411.07645
66 1938 25.145.697.104.636.357.696.39423
632.306.082.878.117.302.583.050.385.203.711.878.280.603.23645
65 1937 20.706.193.716.777.033.766.26823
428.746.458.236.696.712.033.040.330.217.696.632.854.647.82445
64 1934 12.093.315.807.217.013.334.12123
146.248.287.213.084.882.816.757.618.288.480.312.782.842.64145
63 1554 3.036.233.455.854.775.865.62322
9.218.713.598.451.835.185.192.915.815.381.548.953.178.12943
62 1553 2.211.007.906.320.264.673.87822
4.888.555.961.810.720.288.016.108.820.270.181.695.558.88443
61 1552 2.016.192.509.426.760.663.59822
4.065.032.235.068.578.387.346.437.838.758.605.322.305.60443
60 1550 1.121.621.184.033.823.231.53922
1.258.034.080.473.435.562.012.102.655.343.740.804.308.52143
59 1372 263.397.138.410.176.890.08621
69.378.052.522.669.882.013.031.028.896.622.525.087.39641
58 1371 260.088.804.053.044.407.02621
67.646.185.993.742.928.767.376.782.924.739.958.164.67641
57 1370 229.359.782.235.085.482.22521
52.605.909.706.925.833.964.246.933.852.960.790.950.62541
56 1367 128.501.150.236.577.373.66921
16.512.545.612.123.429.216.861.292.432.121.654.521.56141
55 1081 25.686.162.978.506.292.36620
659.778.968.558.387.244.939.442.783.855.869.877.95639
54 949 2.282.211.769.458.230.80519
5.208.490.560.653.668.833.388.663.560.650.948.02537
53 946 1.363.859.210.193.543.29119
1.860.111.945.229.755.699.965.579.225.491.110.68137
52 737 306.950.094.269.977.05718
94.218.360.372.347.802.120.874.327.306.381.24935
51 736 228.138.929.476.341.40518
52.047.371.142.611.077.177.011.624.117.374.02535
50 735 207.254.460.945.174.61818
42.954.411.581.674.911.011.947.618.511.445.92435
49 733 135.772.344.267.730.05918
18.434.129.467.955.011.411.055.976.492.143.48135
48 636 13.661.181.333.262.45917
186.627.875.420.278.656.872.024.578.726.68133
47 635 13.593.470.459.544.30917
184.782.439.134.503.767.305.431.934.287.48133
46 634 12.797.593.520.483.48117
163.778.399.915.520.777.025.519.993.877.36133
45 633 11.863.792.420.598.92917
140.749.570.599.060.595.060.995.075.947.04133
44 632 11.843.191.515.764.82117
140.261.185.279.083.838.380.972.581.162.04133
43 484 3.138.199.296.186.06716
9.848.294.822.582.726.272.852.284.928.48931
42 483 3.107.974.295.870.66316
9.659.504.223.792.743.472.973.224.059.56931
41 482 3.066.446.727.654.24316
9.403.095.533.541.415.141.453.355.903.04931
40 481 2.564.053.868.197.73416
6.574.372.239.019.762.679.109.322.734.75631
39 480 2.201.019.508.986.47816
4.844.486.878.939.076.709.398.786.844.48431
38 414 314.155.324.482.86715
98.693.567.900.935.453.900.976.539.68929
37 413 210.786.628.549.53815
44.431.002.775.280.908.257.720.013.44429
36 410 129.610.990.752.56915
16.799.008.923.862.526.832.980.099.76129
35 307 30.395.080.190.57314
923.860.899.791.363.197.998.068.32927
34 262 3.069.306.930.69313
9.420.645.034.800.084.305.460.24925
33 261 2.634.812.417.86413
6.942.236.477.330.337.746.322.49625
32 260 2.149.099.165.35813
4.618.627.222.542.452.227.268.16425
31 257 1.349.465.117.84113
1.821.056.104.269.624.016.501.28125
30 191 128.817.084.66912
16.593.841.302.620.314.839.56123
29 190 112.247.658.96112
12.599.536.942.224.963.599.52123
28 189 111.283.619.36112
12.384.043.938.083.934.048.32123
27 177 101.116.809.85112
10.224.609.234.443.290.642.20123
26 160 30.693.069.30711
942.064.503.484.305.460.24921
25 159 30.101.273.64711
906.086.675.171.576.680.60921
24 158 22.865.150.13511
522.815.090.696.090.518.22521
23 155 13.579.355.05911
184.398.883.818.388.893.48121
22 136 10.207.355.54911
104.190.107.303.701.091.40121
21 129 10.106.064.39911
102.132.537.636.735.231.20121
20 112 2.481.623.25410
6.158.453.974.793.548.51619
19 111 2.062.386.21810
4.253.436.912.196.343.52419
18 94 306.930.6939
94.206.450.305.460.24917
17 68 30.001.2538
900.075.181.570.00915
16 66 12.866.6698
165.551.171.155.56115
15 65 12.028.2298
144.678.292.876.44115
14 64 11.129.3618
123.862.676.268.32115
13 55 3.069.3077
9.420.645.460.24913
12 54 2.294.6757
5.265.533.355.62513
11 53 2.012.7487
4.051.154.511.50413
10 50 1.270.8697
1.615.108.015.16113
9 43 1.042.1517
1.086.078.706.80113
8 30 30.6935
942.060.2499
7 29 24.8465
617.323.7169
6 28 22.8655
522.808.2259
5 19 2.6364
6.948.4967
4 18 2.2854
5.221.2257
3 13 3073
94.2495
2 12 2643
69.6965
1 6 262
6763


















Palindromic Squares with “Non_Palindromic” CORE Basenumbers
[TOP OF PAGE] [SUBSET A] [SUBSET B]
          
rood Full Listing


Serial
Number
Index Pseudopalindromic basenumberLength
Palindromic Square NumberLength
   
See also Sloane's A007573
73 1917 11.100.000.000.910.000.000.11123
123.210.000.020.202.000.003.292.300.000.202.020.000.012.32145
72 1864 11.000.010.000.910.001.000.01123
121.000.220.020.120.040.201.090.102.040.021.020.022.000.12145
71 1841 11.000.000.000.910.000.000.01123
121.000.000.020.020.000.001.070.100.000.020.020.000.000.12145
70 1811 10.101.000.009.901.000.010.10123
102.030.201.200.020.002.302.090.203.200.020.002.102.030.20145
69 1768 10.100.000.010.911.000.000.10123
102.010.000.220.402.200.121.090.121.002.204.022.000.010.20145
68 1765 10.100.000.009.901.000.000.10123
102.010.000.200.000.200.100.070.001.002.000.002.000.010.20145
67 1729 10.010.010.099.900.101.001.00123
100.200.302.200.102.030.022.090.220.030.201.002.203.002.00145
66 1720 10.010.001.099.900.110.001.00123
100.200.122.020.001.412.000.292.000.214.100.020.221.002.00145
65 1707 10.010.000.099.900.100.001.00123
100.200.102.000.000.012.000.070.000.210.000.000.201.002.00145
64 1673 10.001.001.099.900.110.010.00123
100.020.023.000.203.210.200.292.002.012.302.000.320.020.00145
63 1670 10.001.001.009.901.010.010.00123
100.020.021.200.041.022.120.090.021.220.140.002.120.020.00145
62 1665 10.001.000.999.900.010.010.00123
100.020.021.000.001.000.020.070.020.000.100.000.120.020.00145
61 1645 10.000.110.099.900.101.100.00123
100.002.202.010.124.010.002.292.200.010.421.010.202.200.00145
60 1640 10.000.110.000.910.001.100.00123
100.002.200.030.300.222.201.090.102.222.003.030.002.200.00145
59 1637 10.000.109.999.900.001.100.00123
100.002.200.010.100.000.000.272.000.000.001.010.002.200.00145
58 1352 111.000.000.091.000.000.11121
12.321.000.020.202.000.032.923.000.020.202.000.012.32141
57 1315 110.001.000.091.000.100.01121
12.100.220.021.020.204.010.901.040.202.012.002.200.12141
56 1292 110.000.000.091.000.000.01121
12.100.000.020.020.000.010.701.000.002.002.000.000.12141
55 1266 101.010.000.990.100.010.10121
10.203.020.300.020.005.020.902.050.002.000.302.030.20141
54 1255 101.001.000.990.100.100.10121
10.201.202.201.002.201.400.900.410.220.010.220.210.20141
53 1246 101.000.100.990.101.000.10121
10.201.020.400.010.601.020.902.010.601.000.402.010.20141
52 1233 101.000.001.091.100.000.10121
10.201.000.220.402.201.210.901.210.220.402.200.010.20141
51 1230 101.000.000.990.100.000.10121
10.201.000.200.000.201.000.700.010.200.000.200.010.20141
50 1208 100.101.009.990.010.101.00121
10.020.212.201.020.102.040.904.020.102.010.221.202.00141
49 1199 100.100.109.990.011.001.00121
10.020.032.020.012.300.202.920.200.321.002.023.002.00141
48 1186 100.100.009.990.010.001.00121
10.020.012.000.000.102.000.700.020.100.000.021.002.00141
47 1174 100.011.099.990.001.110.00121
10.002.220.121.210.000.024.942.000.001.212.102.220.00141
46 1163 100.010.109.990.011.010.00121
10.002.022.100.214.100.022.922.000.141.200.122.020.00141
45 1160 100.010.100.990.101.010.00121
10.002.020.300.050.203.020.902.030.205.000.302.020.00141
44 1155 100.010.099.990.001.010.00121
10.002.020.100.010.000.020.702.000.001.000.102.020.00141
43 933 1.110.000.009.100.000.11119
1.232.100.020.202.000.329.230.002.020.200.012.32137
42 902 1.100.010.009.100.100.01119
1.210.022.020.120.402.109.012.040.210.202.200.12137
41 887 1.100.000.009.100.000.01119
1.210.000.020.020.000.107.010.000.200.200.000.12137
40 865 1.010.100.099.010.010.10119
1.020.302.210.020.032.209.022.300.200.122.030.20137
39 844 1.010.000.109.110.000.10119
1.020.100.220.402.212.109.012.122.040.220.010.20137
38 841 1.010.000.099.010.000.10119
1.020.100.200.000.210.007.000.120.000.020.010.20137
37 811 1.001.000.999.001.001.00119
1.002.003.000.001.002.007.002.001.000.003.002.00137
36 797 1.000.110.099.010.110.00119
1.000.220.210.142.012.029.202.102.410.120.220.00137
35 794 1.000.110.009.100.110.00119
1.000.220.030.302.222.109.012.222.030.300.220.00137
34 791 1.000.109.999.000.110.00119
1.000.220.010.100.000.027.200.000.010.100.220.00137
33 621 11.100.000.910.000.11117
123.210.020.202.003.292.300.202.020.012.32133
32 602 11.001.000.910.010.01117
121.022.021.022.041.090.140.220.120.220.12133
31 587 11.000.000.910.000.01117
121.000.020.020.001.070.100.020.020.000.12133
30 569 10.101.009.901.010.10117
102.030.401.020.304.090.403.020.104.030.20133
29 562 10.100.109.901.100.10117
102.012.220.014.300.292.003.410.022.210.20133
28 555 10.100.010.911.000.10117
102.010.220.402.321.090.123.204.022.010.20133
27 552 10.100.009.901.000.10117
102.010.200.000.300.070.003.000.002.010.20133
26 544 10.011.099.900.111.00117
100.222.121.210.002.494.200.012.121.222.00133
25 535 10.010.109.901.101.00117
100.202.300.232.120.292.021.232.003.202.00133
24 530 10.010.099.900.101.00117
100.202.100.010.002.070.200.010.001.202.00133
23 401 111.000.091.000.11115
12.321.020.202.032.923.020.202.012.32129
22 386 110.010.091.010.01115
12.102.220.124.030.903.042.102.220.12129
21 377 110.000.091.000.01115
12.100.020.020.010.701.002.002.000.12129
20 363 101.010.990.110.10115
10.203.220.123.022.922.032.102.230.20129
19 356 101.001.091.100.10115
10.201.220.403.410.901.430.402.210.20129
18 353 101.000.990.100.10115
10.201.200.001.200.700.210.000.210.20129
17 345 100.110.990.111.00115
10.022.210.341.004.940.014.301.222.00129
16 342 100.110.091.011.00115
10.022.030.322.230.903.222.303.022.00129
15 339 100.109.990.011.00115
10.022.010.100.002.720.000.101.022.00129
14 250 1.110.009.100.11113
1.232.120.202.329.232.020.212.32125
13 243 1.101.009.101.01113
1.212.221.040.509.050.401.222.12125
12 234 1.100.009.100.01113
1.210.020.020.107.010.200.200.12125
11 228 1.011.099.011.10113
1.022.321.210.249.420.121.232.20125
10 221 1.010.109.110.10113
1.020.320.414.309.034.140.230.20125
9 218 1.010.099.010.10113
1.020.300.010.207.020.100.030.20125
8 150 11.100.910.11111
123.230.205.292.502.032.32121
7 145 11.010.911.01111
121.240.161.292.161.042.12121
6 140 11.000.910.01111
121.020.021.070.120.020.12121
5 133 10.110.911.10111
102.230.523.292.325.032.20121
4 130 10.109.901.10111
102.210.100.272.001.012.20121
3 89 111.091.1119
12.341.234.943.214.32117
2 84 110.091.0119
12.120.030.703.002.12117
1 47 1.109.1117
1.230.127.210.32113



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( © All rights reserved ) - Last modified : October 27, 2016.
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E-mail address : pdg@worldofnumbers.com