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Palindromic Sums of Squares of
Consecutive Odd & Even Numbers
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rood Palindromes in other Bases rood Palindromes in Concatenations


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 : 353, 37173, 24611642

Sums of Squares of TWO Consecutive Odd & Even Numbers
Sums of Squares of THREE Consecutive Odd & Even Integers
Sums of Squares of FOUR Consecutive Odd & Even Integers
Sums of Squares of FIVE Consecutive Odd & Even Integers
Sums of Squares of SIX Consecutive Odd & Even Integers
Sums of Squares of SEVEN Consecutive Odd & Even Integers
Sums of Squares of EIGHT Consecutive Odd & Even Integers
Sums of Squares of NINE Consecutive Odd & Even Integers
Sums of Squares of TEN Consecutive Odd & Even Integers
Sums of Squares of ELEVEN Consecutive Odd & Even Integers


     PLAIN TEXT SUMSQUARE OE 

Sums of Squares O&EChange of variablesCUDApalin parametersBase Correction
2 termsn.a.
A B C →  2 4 4
base = CUDAbase
3 termsn.a.
A B C →  3 12 20
base = CUDAbase
4 termsn.a.
A B C →  4 24 56
base = CUDAbase
5 termsn.a.
A B C →  5 40 120
base = CUDAbase
6 termsn.a.
A B C →  6 60 220
base = CUDAbase
7 termsn.a.
A B C →  7 84 364
base = CUDAbase
8 termsn.a.
A B C →  8 112 560
base = CUDAbase
9 termsn.a.
A B C →  9 144 816
base = CUDAbase
10 termsn.a.
A B C →  10 180 1140
base = CUDAbase
11 termsn.a.
A B C →  11 220 1540
base = CUDAbase

The sequence for parameter 'A' is 2, 3, 4, 5, ... [+ 1]
The 'B' CUDApalin parameters are given by A046092 → 4 times triangular numbers: a(n) = 2*n*(n+1).
The 'C' CUDApalin parameters are given by A002492 → Sum of the first n even squares: 2*n*(n+1)*(2*n+1)/3.

Sums of TWO squared odd or even consecutives of the form 2*x^2 + 4*x + 4 can only start or end with a 0, 2 or 4.
Alas, my palindromes may not have leading 0's! So the zero option must not be investigated.
2 can only be followed by a 0 or 5 : 20 or 25
4 can be followed by any number : 40, 41, 42, 43, 44, 45, 46, 47, 48 or 49
bu17 There are no palindromic sums of squares of type [SUSQOE2] of EVEN lengths. All ODD lengths ⩽ 55 are represented.

Sums of THREE squared odd or even consecutives of the form 3*x^2 + 12*x + 20 can only start or end with a 0, 1, 3, 5, 6 or 8.
Alas, my palindromes may not have leading 0's! So the zero option must not be investigated.
1 can only be followed by an odd number : 11, 13, 15, 17 or 19
3 can only be followed by 8 : 38
5 can only be followed by an odd number : 51, 53, 55, 57 or 59
6 can only be followed by an odd number : 61, 63, 65, 67 or 69
8 can only be followed by 0 : 80
bu17 There are no palindromic sums of squares of type [SUSQOE3] of lengths 1, 2, 10, 14, 18, 22, 27, 30, {33 up to 36}, 38, 41, 43, 45, 50, 52, 54.

Sums of FOUR squared odd or even consecutives of the form 4*x^2 + 12*x + 20 can only start or end with a 0, 1, 3, 5, 6 or 8.
Alas, my palindromes may not have leading 0's! So the zero option must not be investigated.
4 can only be followed by an even number : 40, 42, 44, 46 or 48
6 can only be followed by an odd number : 61, 63, 65, 67 or 69
bu17 There are no palindromic sums of squares of type [SUSQOE4] of EVEN lengths nor ODD lengths 1, 7, 15, 31, 33, 37, 39, 43, 51, 55.

Sums of FIVE squared odd or even consecutives of the form 5*x^2 + 40*x + 120 can only start or end with a 0 or 5.
Alas, my palindromes may not have leading 0's! So the zero option must not be investigated.
5 can be followed by an even number : 50, 52, 54, 56, 58
bu17 There are no palindromic sums of squares of type [SUSQOE5] of lengths {1 up to 5}, 7, 8, {10 up to 21}, {23 up to 25}, 27, {30 up to 34}, {38 up to 40}, 42, 43, 45, 46, {48 up to 52}, 54, 55.

Sums of SIX squared odd or even consecutives of the form 6*x^2 + 60*x + 220 can only start or end with a 0, 4 or 6.
Alas, my palindromes may not have leading 0's! So the zero option must not be investigated.
4 can be followed by any number : 40, 41, 42, 43, 44, 45, 46, 47, 48 or 49
6 can be followed by any number : 60, 61, 62, 63, 64, 65, 66, 67, 68 or 69
bu17 There are no palindromic sums of squares of type [SUSQOE6] of lengths 1, 2, 5, 10, 11, 13, 14, {16 up to 18}, {20 up to 22}, 25, 26, 29, 32, 33, {35 up to 38}, 42, 44, 46, 48, 50, 51, 53.

Sums of SEVEN squared odd or even consecutives of the form 70*x^2 + 84*x + 364 can only start or end with a 0, 1, 3, 5, 6 or 8.
Alas, my palindromes may not have leading 0's! So the zero option must not be investigated.
2 can only be followed by 1 : 21
4 can only be followed by an even number : 40, 42, 44, 46 or 48
5 can only be followed by an odd number : 51, 53, 55, 57 or 59
7 can only be followed by 8 : 78
9 can only be followed by an odd number : 91, 93, 95, 97 or 99
bu17 There are no palindromic sums of squares of type [SUSQOE7] of EVEN lengths nor ODD lengths 1, 5, 7, 11, 17, 23, 25, 29, 33, 37, 39, 45, 47, 55.

Sums of EIGHT squared odd or even consecutives of the form 8*x^2 + 112*x + 560 can only start or end with a 0, 6 or 8.
Alas, my palindromes may not have leading 0's! So the zero option must not be investigated.
6 can only be followed by an odd number : 61, 63, 65, 67 or 69
8 can only be followed by 6 : 86
bu17 There are no palindromic sums of squares of type [SUSQOE8] of lengths {1 up to 4}, {6 up to 18}, {21 up to 24}, 26, 29, 31, 32, 34, 36, {38 up to 42}, {44 up to 46}, {48 up to 50}, {52 up to 55}.

Sums of NINE squared odd or even consecutives of the form 9*x^2 + 144*x + 816 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 6 : 56
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
bu17 There are no palindromic sums of squares of type [SUSQOE9] of EVEN lengths nor ODD lengths 1, 5, 7, 13, 15, 21, 25, 31, 37, {41 up to 47}, {51 up to 55}.

Sums of TEN squared odd or even consecutives of the form 10*x^2 + 180*x + 1140 can only start or end with a 0.
Alas, my palindromes may not have leading 0's! So the zero option must not be investigated.
As there are no other ending digits we conclude that there exist no palindromic sums of squares of type [SUSQOE10].
Cudapalin quote → "F(x) ends with zero for all inputs - no palindromes exist!"
bu17 There are no palindromic sums of squares of type [SUSQOE10] of any lengths.

Sums of ELEVEN squared odd or even consecutives of the form 11*x^2 + 220*x + 1540 can only start or end with a 0, 1, 4, 5, 6 or 9.
Alas, my palindromes may not have leading 0's! So the zero option must not be investigated.
1 can only be followed by an odd number : 11, 13, 15, 17 or 19
4 can only be followed by an even number : 40, 42, 44, 46 or 48
5 can only be followed by 1 : 51
6 can only be followed by an odd number : 61, 63, 65, 67 or 69
9 can only be followed by an odd number : 91, 93, 95, 97 or 99
bu17 There are no palindromic sums of squares of type [SUSQOE11] of lengths {1 up to 3}, 7, 9, 17, 23, 29, 31, {41 up to 43}, 47, 50, 51, 53, 55.

A first infinite palindromic pattern hides in the list for case 2*x^2 + 4*x + 4

92 + 112 = 202 [PL=3]
992 + 1012 = 20002 [PL=5]
9992 + 10012 = 2000002 [PL=7]
99992 + 100012 = 200000002 [PL=9]
999992 + 1000012 = 20000000002 [PL=11]
9999992 + 10000012 = 2000000000002 [PL=13]
99999992 + 100000012 = 200000000000002 [PL=15]
999999992 + 1000000012 = 20000000000000002 [PL=17]
9999999992 + 10000000012 = 2000000000000000002 [PL=19]

A second infinite palindromic pattern hides in the same list

10192 + 10212 = 2080802 [PL=7]
10001992 + 10002012 = 2000800080002 [PL=13]
10000019992 + 10000020012 = 2000008000008000002 [PL=19]
1000000019992 + 10000000200012 = 2000000080000000800000002 [PL=25]
1000000000199992 + 10000000002000012 = 2000000000800000000080000000002 [PL=31]
1000000000001999992 + 10000000000020000012 = 2000000000008000000000008000000000002 [PL=37]
1000000000000019999992 + 10000000000000200000012 = 2000000000000080000000000000800000000000002 [PL=43]
1000000000000000199999992 + 10000000000000002000000012 = 2000000000000000800000000000000080000000000000002 [PL=49]
1000000000000000001999999992 + 10000000000000000020000000012 = 2000000000000000008000000000000000008000000000000000002 [PL=55]


Palindromic Sums of Squares of Consecutive Odd & Even Numbers


Index Nr Base Sequence ExpressionInitials
Palindromic Sums of Squares of Consecutive Odd & Even Numbers Length 
halt down
[SUSQOE2] Sums of Squares of TWO Consecutive Odd & Even Numbers
2 terms
All entries up to 78 found by Patrick De Geest [ July 27, 2023 ]
No even-length palindromes exist!
781.522.130.358.458.249.532.479.063.7082 + 1.522.130.358.458.249.532.479.063.710228
4.633.761.656.280.478.428.122.744.751.574.472.218.248.740.826.561.673.36455
771.519.214.211.338.771.342.489.408.5082 + 1.519.214.211.338.771.342.489.408.510228
4.616.023.639.867.369.993.387.362.140.412.637.833.999.637.689.363.206.16455
761.429.447.671.315.326.741.664.921.7002 + 1.429.447.671.315.326.741.664.921.702228
4.086.641.290.057.620.788.106.625.859.585.266.018.870.267.500.921.466.80455
751.000.000.000.000.000.001.999.999.9992 + 1.000.000.000.000.000.002.000.000.001228
2.000.000.000.000.000.008.000.000.000.000.000.008.000.000.000.000.000.00255
74999.999.999.999.999.999.999.999.9992 + 1.000.000.000.000.000.000.000.000.001227 - 28
2.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.00255
73100.693.715.110.743.186.027.597.9392 + 100.693.715.110.743.186.027.597.941227
20.278.448.525.607.021.272.747.822.922.874.727.212.070.652.584.487.20253
7299.999.999.999.999.999.999.999.9992 + 100.000.000.000.000.000.000.000.001226 - 27
20.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.00253
7110.208.525.244.586.345.224.584.3192 + 10.208.525.244.586.345.224.584.321226
208.427.975.338.713.399.180.159.121.951.081.993.317.833.579.724.80251
709.999.999.999.999.999.999.999.9992 + 10.000.000.000.000.000.000.000.001225 - 26
200.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.00251
691.544.060.936.260.820.055.567.3432 + 1.544.060.936.260.820.055.567.345225
4.768.248.349.773.280.428.643.594.953.468.240.823.779.438.428.67449
681.001.271.646.275.738.735.260.9492 + 1.001.271.646.275.738.735.260.951225
2.005.089.819.271.456.141.434.822.284.341.416.541.729.189.805.00249
671.000.000.000.000.000.199.999.9992 + 1.000.000.000.000.000.200.000.001225
2.000.000.000.000.000.800.000.000.000.000.080.000.000.000.000.00249
66999.999.999.999.999.999.999.9992 + 1.000.000.000.000.000.000.000.001224 - 25
2.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.00249
6599.999.999.999.999.999.999.9992 + 100.000.000.000.000.000.000.001223 - 24
20.000.000.000.000.000.000.000.000.000.000.000.000.000.000.00247
6415.224.465.099.312.678.270.5402 + 15.224.465.099.312.678.270.542223
46356867512037959727046407279597302157686536445
6310.068.969.006.152.918.048.4392 + 10.068.969.006.152.918.048.441223
202.768.273.693.736.164.432.848.234.461.637.396.372.867.20245
629.999.999.999.999.999.999.9992 + 10.000.000.000.000.000.000.001222 - 23
200.000.000.000.000.000.000.000.000.000.000.000.000.000.00245
611.000.000.000.000.019.999.9992 + 1.000.000.000.000.020.000.001222
2.000.000.000.000.080.000.000.000.000.800.000.000.000.00243
60999.999.999.999.999.999.9992 + 1.000.000.000.000.000.000.001221 - 22
2.000.000.000.000.000.000.000.000.000.000.000.000.000.00243
59147.124.387.475.601.516.2952 + 147.124.387.475.601.516.297221
43.291.170.780.141.864.617.671.646.814.108.707.119.23441
5899.999.999.999.999.999.9992 + 100.000.000.000.000.000.001220 - 21
20.000.000.000.000.000.000.000.000.000.000.000.000.00241
5715.065.605.139.479.625.4732 + 15.065.605.139.479.625.475220
453.944.916.437.429.810.666.018.924.734.619.449.35439
569.999.999.999.999.999.9992 + 10.000.000.000.000.000.001219 - 20
200.000.000.000.000.000.000.000.000.000.000.000.00239
551.000.000.000.001.999.9992 + 1.000.000.000.002.000.001219
2.000.000.000.008.000.000.000.008.000.000.000.00237
54999.999.999.999.999.9992 + 1.000.000.000.000.000.001218 - 19
2.000.000.000.000.000.000.000.000.000.000.000.00237
53141.504.969.544.687.7482 + 141.504.969.544.687.750218
40.047.312.811.686.014.741.068.611.821.374.00435
5299.999.999.999.999.9992 + 100.000.000.000.000.001217 - 18
20.000.000.000.000.000.000.000.000.000.000.00235
5111.185.524.826.864.3542 + 11.185.524.826.864.356217
250.231.931.304.797.717.797.403.139.132.05233
5010.210.939.561.531.2692 + 10.210.939.561.531.271217
208.526.573.458.488.808.884.854.375.625.80233
499.999.999.999.999.9992 + 10.000.000.000.000.001216 - 17
200.000.000.000.000.000.000.000.000.000.00233
481.417.954.293.217.1982 + 1.417.954.293.217.200216
4.021.188.755.306.172.716.035.578.811.20431
471.415.627.973.247.9982 + 1.415.627.973.247.998216
4.008.005.117.284.474.744.827.115.008.00431
461.019.867.707.701.5192 + 1.019.867.707.701.521216
2.080.260.282.424.706.074.242.820.620.80231
451.006.660.477.511.4092 + 1.006.660.477.511.411216
2.026.730.633.966.999.996.693.360.376.20231
441.000.000.000.199.9992 + 1.000.000.000.200.001216
2.000.000.000.800.000.000.080.000.000.00231
43999.999.999.999.9992 + 1.000.000.000.000.001215 - 16
2.000.000.000.000.000.000.000.000.000.00231
42146.775.992.523.0032 + 146.775.992.523.005215
43.086.383.962.225.852.226.938.368.03429
41142.168.071.671.8982 + 142.168.071.671.900215
40.423.521.205.812.421.850.212.532.40429
40102.154.806.312.1692 + 102.154.806.312.171215
20.871.208.905.353.935.350.980.217.80229
39100.731.171.537.6392 + 100.731.171.537.641215
20.293.537.838.690.909.683.873.539.20229
3899.999.999.999.9992 + 100.000.000.000.001214 - 15
20.000.000.000.000.000.000.000.000.00229
379.999.999.999.9992 + 10.000.000.000.001213 - 14
200.000.000.000.000.000.000.000.00227
361.483.852.810.0382 + 1.483.852.810.040213
4.403.638.323.721.273.238.363.04425
351.020.214.285.5292 + 1.020.214.285.531213
2.081.674.376.798.976.734.761.80225
341.000.013.706.4992 + 1.000.013.706.501213
2.000.054.826.375.736.284.500.00225
331.000.000.019.9992 + 1.000.000.020.001213
2.000.000.080.000.000.800.000.00225
32999.999.999.9992 + 1.000.000.000.001212 - 13
2.000.000.000.000.000.000.000.00225
31147.701.737.1032 + 147.701.737.105212
43.631.606.287.078.260.613.63423
30100.020.249.6992 + 100.020.249.701212
20.008.100.700.100.700.180.00223
2999.999.999.9992 + 100.000.000.001211 - 12
20.000.000.000.000.000.000.00223
2814.447.238.4332 + 14.447.238.435211
417.445.396.737.693.544.71421
2714.348.913.1652 + 14.348.913.167211
411.782.618.090.816.287.11421
2611.228.636.5742 + 11.228.636.576211
252.164.558.666.855.461.25221
2510.057.124.6892 + 10.057.124.691211
202.291.514.060.415.192.20221
249.999.999.9992 + 10.000.000.001210 - 11
200.000.000.000.000.000.00221
231.441.760.7332 + 1.441.760.735210
4.157.348.028.208.437.51419
221.120.007.1542 + 1.120.007.156210
2.508.832.054.502.388.05219
211.000.001.9992 + 1.000.002.001210
2.000.008.000.008.000.00219
20999.999.9992 + 1.000.000.00129 - 10
2.000.000.000.000.000.00219
19155.606.1702 + 155.606.17229
48.426.560.906.562.48417
1899.999.9992 + 100.000.00128 - 9
20.000.000.000.000.00217
1715.161.6752 + 15.161.67728
459.752.838.257.95415
169.999.9992 + 10.000.00127 - 8
200.000.000.000.00215
151.442.0152 + 1.442.01727
4.158.820.288.51413
141.128.3642 + 1.128.36627
2.546.415.146.45213
131.000.1992 + 1.000.20127
2.000.800.080.00213
12999.9992 + 1.000.00126 - 7
2.000.000.000.00213
11152.8902 + 152.89226
46.751.315.76411
10141.4982 + 141.50026
40.043.934.00411
9100.6092 + 100.61126
20.244.744.20211
899.9992 + 100.00125 - 6
20.000.000.00211
711.1942 + 11.19625
250.656.0529
69.9992 + 10.00124 - 5
200.000.0029
51.0192 + 1.02124
2.080.8027
49992 + 1.00123 - 4
2.000.0027
3992 + 10122 - 3
20.0025
292 + 1121 - 2
2023
102 + 221
41
up down
[SUSQOE3] Sums of Squares of THREE Consecutive Odd & Even Numbers
3 terms
Entries 3 & 4 by Kimberly Pellechi [ July 1, 2003 ]
Odd entries up to 22 by Patrick De Geest [ July 7, 2003 ]
Even entries 13, 15 and 19 found by Patrick De Geest [ July 13, 2003 ]
All entries above 22 up to 57 found by Patrick De Geest [ July 25, 2023 ]
Entries 58 & 59 added by Patrick De Geest [ July 28, 2023 ]
591.340.257.503.315.181.526.037.061.6012 + 1.340.257.503.315.181.526.037.061.6032 +
1.340.257.503.315.181.526.037.061.6052		28
5.388.870.525.577.931.457.766.988.200.028.896.677.541.397.755.250.788.83555
58607.345.597.940.104.847.140.510.9992 + 607.345.597.940.104.847.140.511.0012 +
607.345.597.940.104.847.140.511.0032		27
1.106.606.026.011.670.467.426.275.751.575.726.247.640.761.106.206.066.01155
57136.381.697.837.985.191.083.563.8052 + 136.381.697.837.985.191.083.563.8072 +
136.381.697.837.985.191.083.563.8092		27
55.799.902.515.514.483.631.731.746.264.713.713.638.441.551.520.999.75553
567.181.186.981.708.430.258.313.1892 + 7.181.186.981.708.430.258.313.1912 +
7.181.186.981.708.430.258.313.1932		25
154.708.339.398.775.903.972.176.545.671.279.309.577.893.933.807.45151
55676.368.730.731.942.874.123.9192 + 676.368.730.731.942.874.123.9212 +
676.368.730.731.942.874.123.9232		24
1.372.423.979.735.818.334.829.698.969.284.338.185.379.793.242.73149
54611.189.734.639.268.865.075.4492 + 611.189.734.639.268.865.075.4512 +
611.189.734.639.268.865.075.4532		24
1.120.658.675.185.259.674.825.674.765.284.769.525.815.768.560.21149
53422.867.819.014.102.027.614.0452 + 422.867.819.014.102.027.614.0472 +
422.867.819.014.102.027.614.0492		24
536.451.577.073.230.044.964.375.573.469.440.032.370.775.154.63548
52244.722.826.032.956.257.063.6372 + 244.722.826.032.956.257.063.6392 +
244.722.826.032.956.257.063.6412		24
179.667.784.744.669.718.181.235.532.181.817.966.447.487.766.97148
51141.172.264.031.151.054.564.3252 + 141.172.264.031.151.054.564.3272 +
141.172.264.031.151.054.564.3292		24
59.788.824.395.043.077.395.912.621.959.377.034.059.342.888.79547
5020.969.457.537.583.825.664.6772 + 20.969.457.537.583.825.664.6792 +
20.969.457.537.583.825.664.6812		23
1.319.154.448.261.593.364.015.005.104.633.951.628.444.519.13146
495.187.439.045.509.399.081.0282 + 5.187.439.045.509.399.081.0302 +
5.187.439.045.509.399.081.0322		22
80.728.571.552.626.396.170.311.307.169.362.625.517.582.70844
482.418.523.162.845.810.905.0372 + 2.418.523.162.845.810.905.0392 +
2.418.523.162.845.810.905.0412		22
17.547.762.867.665.114.321.200.212.341.156.676.826.774.57144
47244.339.546.746.092.833.8592 + 244.339.546.746.092.833.8612 +
244.339.546.746.092.833.8632		21
179.105.442.312.258.255.466.664.552.852.213.244.501.97142
4635.603.928.379.476.184.1532 + 35.603.928.379.476.184.1552 +
35.603.928.379.476.184.1572		20
3.802.919.148.152.608.862.222.688.062.518.419.192.08340
4513.577.239.491.094.710.6412 + 13.577.239.491.094.710.6432 +
13.577.239.491.094.710.6452		20
553.024.296.595.625.271.737.172.526.595.692.420.35539
44805.326.056.917.044.6172 + 805.326.056.917.044.6192 + 805.326.056.917.044.621218
1.945.650.173.848.664.967.694.668.483.710.565.49137
43629.804.761.295.338.2992 + 629.804.761.295.338.3012 + 629.804.761.295.338.303218
1.189.962.112.050.834.171.714.380.502.112.699.81137
421.922.372.986.071.9972 + 1.922.372.986.071.9992 + 1.922.372.986.072.001216
11.086.553.692.738.122.183.729.635.568.01132
411.502.235.864.672.5142 + 1.502.235.864.672.5162 + 1.502.235.864.672.518216
6.770.137.779.325.145.415.239.777.310.77631
401.310.848.278.426.9852 + 1.310.848.278.426.9872 + 1.310.848.278.426.989216
5.154.969.627.164.986.894.617.269.694.51531
39150.367.639.352.6322 + 150.367.639.352.6342 + 150.367.639.352.636215
67.831.280.893.451.415.439.808.213.87629
3851.714.999.614.6182 + 51.714.999.614.6202 + 51.714.999.614.622214
8.023.323.555.420.440.245.553.233.20828
3735.969.637.138.4232 + 35.969.637.138.4252 + 35.969.637.138.427214
3.881.444.387.609.889.067.834.441.88328
362.287.587.433.8892 + 2.287.587.433.8912 + 2.287.587.433.893213
15.699.168.803.088.030.886.199.65126
35796.710.975.7672 + 796.710.975.7692 + 796.710.975.771212
1.904.245.136.732.376.315.424.09125
34359.076.923.2132 + 359.076.923.2152 + 359.076.923.217212
386.808.710.356.653.017.808.68324
33212.711.477.5272 + 212.711.477.5292 + 212.711.477.531212
135.738.518.017.710.815.837.53124
3271.818.181.8072 + 71.818.181.8092 + 71.818.181.811211
15.473.553.715.051.735.537.45123
3113.604.832.2052 + 13.604.832.2072 + 13.604.832.209211
154.735.537.585.735.537.45121
307.181.818.1892 + 7.181.818.1912 + 7.181.818.193210
154.735.537.585.735.537.45121
295.186.766.6282 + 5.186.766.6302 + 5.186.766.632210
80.707.644.222.244.670.70820
283.560.483.8932 + 3.560.483.8952 + 3.560.483.897210
38.031.136.699.663.113.08320
271.640.752.8282 + 1.640.752.8302 + 1.640.752.83229
8.076.209.547.459.026.70819
261.519.030.0622 + 1.519.030.0642 + 1.519.030.06629
6.922.357.006.007.532.29619
251.503.953.1322 + 1.503.953.1342 + 1.503.953.13629
6.785.625.087.805.265.87619
241.404.331.7212 + 1.404.331.7232 + 1.404.331.72529
5.916.442.764.672.446.19519
231.330.011.7452 + 1.330.011.7472 + 1.330.011.74929
5.306.793.741.473.976.03519
2271.818.1892 + 71.818.1912 + 71.818.19328
15.473.557.675.537.45117
2167.315.7192 + 67.315.7212 + 67.315.72328
13.594.218.881.249.53117
2041.386.1352 + 41.386.1372 + 41.386.13928
5.138.437.007.348.31516
1916.403.4682 + 16.403.4702 + 16.403.47228
807.221.484.122.70815
188.008.8172 + 8.008.8192 + 8.008.82127
192.423.545.324.29115
177.181.8072 + 7.181.8092 + 7.181.81127
154.735.141.537.45115
16718.1892 + 718.1912 + 718.19326
1.547.394.937.45113
15482.1842 + 482.1862 + 482.18826
697.510.015.79612
14413.8612 + 413.8632 + 413.86526
513.847.748.31512
13145.4242 + 145.4262 + 145.42826
63.446.164.43611
12113.5132 + 113.5152 + 113.51726
38.656.965.68311
1111.3732 + 11.3752 + 11.37725
388.171.8839
106.7192 + 6.7212 + 6.72324
135.515.5319
94.1352 + 4.1372 + 4.13924
51.344.3158
81.1332 + 1.1352 + 1.13724
3.864.6837
77592 + 7612 + 76323
1.737.3717
67072 + 7092 + 71123
1.508.0517
51972 + 1992 + 20123
118.8116
4792 + 812 + 8322
19.6915
3412 + 432 + 4522
5.5554
2192 + 212 + 2322
1.3314
1112 + 132 + 1522
5153
up down
[SUSQOE4] Sums of Squares of FOUR Consecutive Odd & Even Numbers
4 terms
Entries 1 up to 27 added by Patrick De Geest [ July 30, 2023 ]
No even-length palindromes exist!
27108.033.287.665.139.718.661.214.8662 + 108.033.287.665.139.718.661.214.8682 +
108.033.287.665.139.718.661.214.8702 + 108.033.287.665.139.718.661.214.8722		27
46.684.764.974.955.318.739.453.635.053.635.493.781.355.947.946.748.66453
26107.631.130.505.648.865.294.700.3412 + 107.631.130.505.648.865.294.700.3432 +
107.631.130.505.648.865.294.700.3452 + 107.631.130.505.648.865.294.700.3472		27
46.337.841.015.696.071.061.814.148.184.141.816.017.069.651.014.873.36453
251.238.513.787.958.571.133.356.4792 + 1.238.513.787.958.571.133.356.4812 +
1.238.513.787.958.571.133.356.4832 + 1.238.513.787.958.571.133.356.4852		25
6.135.665.611.853.953.995.533.182.813.355.993.593.581.165.665.31649
24109.614.201.638.105.786.624.4932 + 109.614.201.638.105.786.624.4952 +
109.614.201.638.105.786.624.4972 + 109.614.201.638.105.786.624.4992		24
48.061.092.803.037.253.263.280.908.236.235.273.030.829.016.08447
2312.589.538.239.475.731.477.0702 + 12.589.538.239.475.731.477.0722 +
12.589.538.239.475.731.477.0742 + 12.589.538.239.475.731.477.0762		23
633.985.892.332.886.801.461.757.164.108.688.233.298.589.33645
22132.020.235.730.774.135.2852 + 132.020.235.730.774.135.2872 +
132.020.235.730.774.135.2892 + 132.020.235.730.774.135.2912		21
69.717.370.569.636.686.717.271.768.663.696.507.371.79641
21103.448.960.742.834.659.8962 + 103.448.960.742.834.659.8982 +
103.448.960.742.834.659.9002 + 103.448.960.742.834.659.9022		21
42.806.749.915.090.186.355.255.368.109.051.994.760.82441
20105.622.713.406.372.7812 + 105.622.713.406.372.7832 +
105.622.713.406.372.7852 + 105.622.713.406.372.7872		18
44.624.630.349.299.044.144.099.294.303.642.64435
19102.890.654.656.4732 + 102.890.654.656.4752 +
102.890.654.656.4772 + 102.890.654.656.4792		15
42.345.947.262.552.825.526.274.954.32429
1812.951.239.750.4552 + 12.951.239.750.4572 +
12.951.239.750.4592 + 12.951.239.750.4612		14
670.938.444.295.373.592.444.839.07627
1710.524.564.980.0062 + 10.524.564.980.0082 +
10.524.564.980.0102 + 10.524.564.980.0122		14
443.065.872.073.727.370.278.560.34427
1610.522.494.421.1632 + 10.522.494.421.1652 +
10.522.494.421.1672 + 10.522.494.421.1692		14
442.891.555.373.878.373.555.198.24427
151.258.096.074.9242 + 1.258.096.074.9262 + 1.258.096.074.9282 + 1.258.096.074.930213
6.331.222.934.986.894.392.221.33625
14102.687.721.8232 + 102.687.721.8252 + 102.687.721.8272 + 102.687.721.829212
42.179.072.855.255.827.097.12423
1312.973.588.2802 + 12.973.588.2822 + 12.973.588.2842 + 12.973.588.286211
673.255.971.747.179.552.37621
121.007.628.4112 + 1.007.628.4132 + 1.007.628.4152 + 1.007.628.417210
4.061.260.082.800.621.60419
11125.684.0202 + 125.684.0222 + 125.684.0242 + 125.684.02629
63.185.894.549.858.13617
101.049.4812 + 1.049.4832 + 1.049.4852 + 1.049.48727
4.405.666.665.04413
91.027.3462 + 1.027.3482 + 1.027.3502 + 1.027.35227
4.221.783.871.22413
8126.2992 + 126.3012 + 126.3032 + 126.30526
63.808.780.83611
7108.2782 + 108.2802 + 108.2822 + 108.28426
46.899.099.86411
613.1342 + 13.1362 + 13.1382 + 13.14025
690.323.0969
512.5952 + 12.5972 + 12.5992 + 12.60125
634.838.4369
410.0862 + 10.0882 + 10.0902 + 10.09225
407.151.7049
310.0832 + 10.0852 + 10.0872 + 10.08925
406.909.6049
21252 + 1272 + 1292 + 13123
65.5565
1102 + 122 + 142 + 1622
6963
up down
[SUSQOE5] Sums of Squares of FIVE Consecutive Odd & Even Numbers
5 terms
Entries 1 up to 3 by Kimberly Pellechi [ July 14, 2003 ]
Entries 4 up to 20 by Patrick De Geest [ August 6, 2023 ]
20104.334.223.622.163.229.266.500.1872 + 104.334.223.622.163.229.266.500.1892 + …
+ 104.334.223.622.163.229.266.500.1932 + 104.334.223.622.163.229.266.500.1952		27
54.428.151.094.197.817.982.346.992.829.964.328.971.879.149.015.182.44553
19105.989.818.978.524.677.892.3112 + 105.989.818.978.524.677.892.3132 + …
+ 105.989.818.978.524.677.892.3172 + 105.989.818.978.524.677.892.3192		24
56.169.208.635.502.149.970.703.630.707.994.120.553.680.296.16547
18104.729.670.125.762.942.552.2772 + 104.729.670.125.762.942.552.2792 + …
+ 104.729.670.125.762.942.552.2832 + 104.729.670.125.762.942.552.2852		24
54.841.519.023.255.614.796.375.057.369.741.655.232.091.514.84547
17104.557.778.375.485.052.525.6072 + 104.557.778.375.485.052.525.6092 + …
+ 104.557.778.375.485.052.525.6132 + 104.557.778.375.485.052.525.6152		24
54.661.645.094.085.248.347.856.865.874.384.258.049.054.616.64547
16104.162.490.995.457.305.204.7752 + 104.162.490.995.457.305.204.7772 + …
+ 104.162.490.995.457.305.204.7812 + 104.162.490.995.457.305.204.7832		24
54.249.122.651.893.620.942.873.637.824.902.639.815.622.194.24547
153.426.250.846.378.183.190.9192 + 3.426.250.846.378.183.190.9212 + …
+ 3.426.250.846.378.183.190.9252 + 3.426.250.846.378.183.190.9272		22
58.695.974.311.536.083.359.144.195.338.063.511.347.959.68544
143.350.173.659.395.709.257.5312 + 3.350.173.659.395.709.257.5332 + …
+ 3.350.173.659.395.709.257.5372 + 3.350.173.659.395.709.257.5392		22
56.118.317.740.544.188.717.944.971.788.144.504.771.381.16544
13108.094.190.860.567.407.0632 + 108.094.190.860.567.407.0652 + …
+ 108.094.190.860.567.407.0692 + 108.094.190.860.567.407.0712		21
58.421.770.489.003.871.775.957.717.830.098.407.712.48541
121.045.775.110.615.561.0572 + 1.045.775.110.615.561.0592 + …
+ 1.045.775.110.615.561.0632 + 1.045.775.110.615.561.0652		19
5.468.227.909.914.944.864.684.494.199.097.228.64537
111.040.174.697.714.113.8972 + 1.040.174.697.714.113.8992 + …
+ 1.040.174.697.714.113.9032 + 1.040.174.697.714.113.9052		19
5.409.817.008.823.241.153.511.423.288.007.189.04537
10330.148.460.133.156.1052 + 330.148.460.133.156.1072 + …
+ 330.148.460.133.156.1112 + 330.148.460.133.156.1132		18
544.990.028.641.470.843.348.074.146.820.099.44536
9107.751.690.425.406.2432 + 107.751.690.425.406.2452 + …
+ 107.751.690.425.406.2492 + 107.751.690.425.406.2512		18
58.052.133.947.662.921.412.926.674.933.125.08535
8106.002.387.084.3212 + 106.002.387.084.3232 + … +
106.002.387.084.3272 + 106.002.387.084.3292		15
56.182.530.337.875.357.873.303.528.16529
733.122.062.601.3772 + 33.122.062.601.3792 + … +
33.122.062.601.3832 + 33.122.062.601.3852		14
5.485.355.154.849.009.484.515.535.84528
63.299.572.679.5372 + 3.299.572.679.5392 + … +
3.299.572.679.5432 + 3.299.572.679.5452		13
54.435.899.337.866.873.399.853.44526
534.069.036.8932 + 34.069.036.8952 + … + 34.069.036.8992 + 34.069.036.901211
5.803.496.375.445.736.943.08522
432.887.839.5472 + 32.887.839.5492 + … + 32.887.839.5532 + 32.887.839.555211
5.408.049.951.661.599.408.04522
310.7892 + 10.7912 + 10.7932 + 10.7952 + 10.79725
582.444.2859
210.3952 + 10.3972 + 10.3992 + 10.4012 + 10.40325
540.696.0459
13312 + 3332 + 3352 + 3372 + 33923
561.1656
up down
[SUSQOE6] Sums of Squares of SIX Consecutive Odd & Even Numbers
6 terms
381.053.147.643.863.626.091.690.252.7992 + 1.053.147.643.863.626.091.690.252.8012 + … +
1.053.147.643.863.626.091.690.252.8072 + 1.053.147.643.863.626.091.690.252.8092		28
6.654.719.758.653.042.093.237.799.676.769.977.323.902.403.568.579.174.56655
37335.267.406.814.796.764.733.957.5442 + 335.267.406.814.796.764.733.957.5462 + … +
335.267.406.814.796.764.733.957.5522 + 335.267.406.814.796.764.733.957.5542		27
674.425.404.433.910.592.737.917.337.733.719.737.295.019.334.404.524.47654
3628.648.591.503.368.851.119.097.0472 + 28.648.591.503.368.851.119.097.0492 + … +
28.648.591.503.368.851.119.097.0552 + 28.648.591.503.368.851.119.097.0572		26
4.924.450.770.761.387.574.492.046.446.402.944.757.831.670.770.544.29452
351.000.720.946.801.709.902.264.2112 + 1.000.720.946.801.709.902.264.2132 + … +
1.000.720.946.801.709.902.264.2192 + 1.000.720.946.801.709.902.264.2212		25
6.008.654.480.206.264.201.593.397.933.951.024.626.020.844.568.00649
34831.073.394.575.048.490.991.4132 + 831.073.394.575.048.490.991.4152 + … +
831.073.394.575.048.490.991.4212 + 831.073.394.575.048.490.991.4232		24
4.144.097.923.022.965.431.457.878.787.541.345.692.203.297.904.41449
3384.222.859.583.409.394.787.3982 + 84.222.859.583.409.394.787.4002 + … +
84.222.859.583.409.394.787.4062 + 84.222.859.583.409.394.787.4082		23
42.560.940.458.440.174.399.656.465.699.347.104.485.404.906.52447
328.717.951.895.177.303.349.9532 + 8.717.951.895.177.303.349.9552 + … +
8.717.951.895.177.303.349.9612 + 8.717.951.895.177.303.349.9632		22
456.016.111.479.753.211.059.262.950.112.357.974.111.610.65445
318.250.142.531.766.319.654.4782 + 8.250.142.531.766.319.654.4802 + … +
8.250.142.531.766.319.654.4862 + 8.250.142.531.766.319.654.4882		22
408.389.110.766.757.472.255.020.552.274.757.667.011.983.80445
301.066.167.557.472.162.364.9892 + 1.066.167.557.472.162.364.9912 + … +
1.066.167.557.472.162.364.9972 + 1.066.167.557.472.162.364.9992		22
6.820.279.563.636.939.837.653.567.389.396.363.659.720.28643
29843.704.983.088.238.398.1422 + 843.704.983.088.238.398.1442 + … +
843.704.983.088.238.398.1502 + 843.704.983.088.238.398.1522		21
4.271.028.590.927.547.848.549.458.487.457.290.958.201.72443
28818.806.905.346.813.604.8782 + 818.806.905.346.813.604.8802 + … +
818.806.905.346.813.604.8862 + 818.806.905.346.813.604.8882		21
4.022.668.489.461.754.643.835.383.464.571.649.848.662.20443
2790.037.834.917.965.011.8822 + 90.037.834.917.965.011.8842 + … +
90.037.834.917.965.011.8902 + 90.037.834.917.965.011.8922		20
48.640.870.300.288.317.353.035.371.388.200.307.804.68441
2625.825.385.908.635.438.9282 + 25.825.385.908.635.438.9302 + … +
25.825.385.908.635.438.9362 + 25.825.385.908.635.438.9382		20
4.001.703.343.979.675.374.774.735.769.793.433.071.00440
2510.362.536.515.455.914.0812 + 10.362.536.515.455.914.0832 + … +
10.362.536.515.455.914.0892 + 10.362.536.515.455.914.0912		20
644.292.978.204.943.187.717.781.349.402.879.292.44639
2410.040.172.062.246.000.4112 + 10.040.172.062.246.000.4132 + … +
10.040.172.062.246.000.4192 + 10.040.172.062.246.000.4212		20
604.830.330.237.030.629.111.926.030.732.033.038.40639
2333.348.510.887.007.4492 + 33.348.510.887.007.4512 + … +
33.348.510.887.007.4572 + 33.348.510.887.007.4592		17
6.672.739.070.285.128.118.215.820.709.372.76634
2232.835.742.368.946.3092 + 32.835.742.368.946.3112 + … +
32.835.742.368.946.3172 + 32.835.742.368.946.3192		17
6.469.115.861.518.896.556.988.151.685.119.64634
211.024.952.883.098.8762 + 1.024.952.883.098.8782 + … +
1.024.952.883.098.8842 + 1.024.952.883.098.8862		16
6.303.170.475.436.250.526.345.740.713.03631
201.024.449.519.721.9212 + 1.024.449.519.721.9232 + … +
1.024.449.519.721.9292 + 1.024.449.519.721.9312		16
6.296.980.910.750.909.090.570.190.896.92631
19259.521.303.414.9122 + 259.521.303.414.9142 + … +
259.521.303.414.9202 + 259.521.303.414.9222		15
404.107.841.557.064.460.755.148.701.40430
1827.528.848.560.7532 + 27.528.848.560.7552 + … +
27.528.848.560.7612 + 27.528.848.560.7632		14
4.547.025.018.486.886.848.105.207.45428
1710.351.110.542.2312 + 10.351.110.542.2332 + … +
10.351.110.542.2392 + 10.351.110.542.2412		14
642.872.936.745.535.547.639.278.24627
16330.937.970.1542 + 330.937.970.1562 + … + 330.937.970.1622 + 330.937.970.164212
657.119.640.557.755.046.911.75624
15106.154.849.2962 + 106.154.849.2982 + … + 106.154.849.3042 + 106.154.849.306212
67.613.112.180.708.121.131.67623
1485.677.010.4222 + 85.677.010.4242 + … + 85.677.010.4302 + 85.677.010.432211
44.043.300.694.249.600.334.04423
131.071.558.1892 + 1.071.558.1912 + … + 1.071.558.1972 + 1.071.558.199210
6.889.421.778.771.249.88619
12856.956.5682 + 856.956.5702 + … + 856.956.5762 + 856.956.57829
4.406.247.408.047.426.04419
1110.712.3012 + 10.712.3032 + … + 10.712.3092 + 10.712.31128
688.520.999.025.88615
1010.023.5612 + 10.023.5632 + … + 10.023.5692 + 10.023.57128
602.831.252.138.20615
9273.3722 + 273.3742 + 273.3762 + 273.3782 + 273.3802 + 273.38226
448.409.904.84412
8259.5782 + 259.5802 + 259.5822 + 259.5842 + 259.5862 + 259.58826
404.300.003.40412
78.8382 + 8.8402 + 8.8422 + 8.8442 + 8.8462 + 8.84824
469.191.9649
62.7182 + 2.7202 + 2.7222 + 2.7242 + 2.7262 + 2.72824
44.488.4448
58122 + 8142 + 8162 + 8182 + 8202 + 82223
4.005.0047
43192 + 3212 + 3232 + 3252 + 3272 + 32923
629.9266
3232 + 252 + 272 + 292 + 312 + 3322
4.7744
2222 + 242 + 262 + 282 + 302 + 3222
4.4444
132 + 52 + 72 + 92 + 112 + 1321 - 2
4543
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[SUSQOE7] Sums of Squares of SEVEN Consecutive Odd & Even Numbers
7 terms
Entries 1 & 2 by Kimberly Pellechi [ July 1 & 25, 2003 ]
Entries 3 up to 16 by Patrick De Geest [ August 7, 2023 ]
No even-length palindromes exist!
1679.318.988.731.618.888.637.097.1682 + 79.318.988.731.618.888.637.097.1702 + … +
79.318.988.731.618.888.637.097.1782 + 79.318.988.731.618.888.637.097.1802		26
44.040.513.813.846.789.624.172.846.864.827.142.698.764.831.831.504.04453
158.118.535.496.287.663.808.785.7882 + 8.118.535.496.287.663.808.785.7902 + … +
8.118.535.496.287.663.808.785.7982 + 8.118.535.496.287.663.808.785.8002		25
461.374.330.231.379.485.908.167.606.761.809.584.973.132.033.473.16451
141.141.123.798.715.161.205.047.4952 + 1.141.123.798.715.161.205.047.4972 + … +
1.141.123.798.715.161.205.047.5052 + 1.141.123.798.715.161.205.047.5072		25
9.115.144.667.958.838.218.385.044.405.838.128.388.597.664.415.11949
131.153.999.382.483.227.426.8632 + 1.153.999.382.483.227.426.8652 + … +
1.153.999.382.483.227.426.8732 + 1.153.999.382.483.227.426.8752		22
9.322.002.023.401.691.597.246.427.951.961.043.202.002.23943
12556.466.714.496.862.897.1442 + 556.466.714.496.862.897.1462 + … +
556.466.714.496.862.897.1542 + 556.466.714.496.862.897.1562		21
2.135.747.251.922.908.459.178.719.548.092.291.527.475.31243
11552.364.689.561.797.757.4342 + 552.364.689.561.797.757.4362 + … +
552.364.689.561.797.757.4442 + 552.364.689.561.797.757.4462		21
2.135.747.251.922.908.459.178.719.548.092.291.527.475.31243
1078.015.699.819.104.718.3982 + 78.015.699.819.104.718.4002 + … +
78.015.699.819.104.718.4082 + 78.015.699.819.104.718.4102		20
42.605.145.927.852.591.943.334.919.525.872.954.150.62441
955.374.962.064.947.0242 + 55.374.962.064.947.0262 + … +
55.374.962.064.947.0342 + 55.374.962.064.947.0362		17
21.464.704.965.860.258.485.206.856.940.746.41235
8810.661.331.084.5502 + 810.661.331.084.5522 + … +
810.661.331.084.5602 + 810.661.331.084.5622		15
4.600.202.556.010.488.840.106.552.020.06431
78.777.698.398.8772 + 8.777.698.398.8792 + … +
8.777.698.398.8872 + 8.777.698.398.8892		13
539.335.924.272.272.272.429.533.93527
68.543.308.3712 + 8.543.308.3732 + … + 8.543.308.3812 + 8.543.308.383210
510.916.826.171.628.619.01521
58884626012 + 888.462.6032 + … + 888.462.6112 + 888.462.61329
5.525.560.628.260.655.25519
45.490.6942 + 5.490.6962 + … + 5.490.7042 + 5.490.70627
211.034.505.430.11215
3552.6342 + 552.6362 + 552.6382 + 552.6402 + 552.6422 + 552.6442 + 552.64626
2.137.876.787.31213
28.5672 + 8.5692 + 8.5712 + 8.5732 + 8.5752 + 8.5772 + 8.57924
514.474.4159
152 + 72 + 92 + 112 + 132 + 152 + 1721 - 2
9593
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[SUSQOE8] Sums of Squares of EIGHT Consecutive Odd & Even Numbers
8 terms
Entries 1 up to 14 by Patrick De Geest [ August 7, 2023 ]
149.186.816.688.499.134.254.020.2172 + 9.186.816.688.499.134.254.020.2192 + … +
9.186.816.688.499.134.254.020.2292 + 9.186.816.688.499.134.254.020.2312		25
675.180.806.944.689.593.064.159.878.951.460.395.986.449.608.081.57651
13103.883.519.028.470.539.980.4732 + 103.883.519.028.470.539.980.4752 + … +
103.883.519.028.470.539.980.4852 + 103.883.519.028.470.539.980.4872		24
86.334.284.205.908.806.102.523.832.520.160.880.950.248.243.36847
1290.319.451.080.212.064.014.1742 + 90.319.451.080.212.064.014.1762 + … +
90.319.451.080.212.064.014.1862 + 90.319.451.080.212.064.014.1882		23
65.260.825.947.446.561.416.874.747.861.416.564.474.952.806.25647
111.037.477.996.217.577.320.5932 + 1.037.477.996.217.577.320.5952 + … +
1.037.477.996.217.577.320.6052 + 1.037.477.996.217.577.320.6072		22
8.610.884.741.085.115.049.196.919.405.115.801.474.880.16843
101.042.434.899.552.978.6782 + 1.042.434.899.552.978.6802 + … +
1.042.434.899.552.978.6902 + 1.042.434.899.552.978.6922		19
8.693.364.158.448.230.084.800.328.448.514.633.96837
990.415.945.425.606.2372 + 90.415.945.425.606.2392 + … +
90.415.945.425.606.2492 + 90.415.945.425.606.2512		17
65.400.345.497.649.653.435.694.679.454.300.45635
89.217.496.450.811.0442 + 9.217.496.450.811.0462 + … +
9.217.496.450.811.0562 + 9.217.496.450.811.0582		16
679.697.926.565.714.575.417.565.629.796.97633
7285.253.951.539.0122 + 285.253.951.539.0142 + … +
285.253.951.539.0242 + 285.253.951.539.0262		15
650.958.534.949.000.000.949.435.859.05630
627.615.302.354.4342 + 27.615.302.354.4362 + … +
27.615.302.354.4462 + 27.615.302.354.4482		14
6.100.839.393.017.557.103.939.380.01628
59.345.561.904.0892 + 9.345.561.904.0912 + … +
9.345.561.904.1012 + 9.345.561.904.1032		13
698.716.218.426.323.624.812.617.89627
4934.383.624.2142 + 934.383.624.2162 + … + 934.383.624.2262 + 934.383.624.228212
6.984.582.057.698.967.502.854.89625
32.762.767.9342 + 2.762.767.9362 + … + 2.762.767.9462 + 2.762.767.948210
61.063.093.566.539.036.01620
2929.013.9142 + 929.013.9162 + … + 929.013.9262 + 929.013.92829
6.904.534.923.294.354.09619
1822 + 842 + 862 + 882 + 902 + 922 + 942 + 9622
635365
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[SUSQOE9] Sums of Squares of NINE Consecutive Odd & Even Numbers
9 terms
Entry 1 by Hugo Sánchez [ March 17, 1999 ]
Entries 2 & 3 by Kimberly Pellechi [ July 25, 2003 ]
Entries 4 up to 15 by Patrick De Geest [ August 8, 2023 ]
No even-length palindromes exist!
15794.780.596.161.835.780.127.2172 + 794.780.596.161.835.780.127.2192 + … +
794.780.596.161.835.780.127.2312 + 794.780.596.161.835.780.127.2332		24
5.685.085.764.318.267.824.341.252.521.434.287.628.134.675.805.86549
147.334.059.368.951.899.5462 + 7.334.059.368.951.899.5482 + … +
7.334.059.368.951.899.5602 + 7.334.059.368.951.899.5622		19
484.095.841.445.800.215.969.512.008.544.148.590.48439
13102.249.539.157.261.5932 + 102.249.539.157.261.5952 + … +
102.249.539.157.261.6072 + 102.249.539.157.261.6092		18
94.094.714.320.851.360.906.315.802.341.749.04935
128.398.580.075.624.6542 + 8.398.580.075.624.6562 + … +
8.398.580.075.624.6682 + 8.398.580.075.624.6702		16
634.825.325.580.115.979.511.085.523.528.43634
1133.679.801.538.0652 + 33.679.801.538.0672 + … +
33.679.801.538.0792 + 33.679.801.538.0812		14
10.208.961.284.795.859.748.216.980.20129
108.404.933.108.5042 + 8.404.933.108.5062 + … +
8.404.933.108.5182 + 8.404.933.108.5202		13
635.786.105.027.050.720.501.687.53627
94.548.265.268.4992 + 4.548.265.268.5012 + … +
4.548.265.268.5132 + 4.548.265.268.5152		13
186.180.452.574.363.475.254.081.68127
83.731.950.732.9392 + 3.731.950.732.9412 + … +
3.731.950.732.9532 + 3.731.950.732.9552		13
125.347.106.458.292.854.601.743.52127
788.157.337.4142 + 88.157.337.4162 + … + 88.157.337.4282 + 88.157.337.430211
69.945.445.272.027.254.454.99623
642.900.264.0292 + 42.900.264.0312 + … + 42.900.264.0432 + 42.900.264.045211
16.563.893.889.998.839.836.56123
5794.460.0672 + 794.460.0692 + … + 794.460.0812 + 794.460.08329
5.680.501.296.921.050.86519
479.044.4272 + 79.044.4292 + … + 79.044.4412 + 79.044.44328
56.232.204.340.223.26517
379.0272 + 79.0292 + … + 79.0412 + 79.04325
56.218.781.26511
23.4652 + 3.4672 + … + 3.4792 + 3.48124
108.555.8019
112 + 32 + 52 + 72 + 92 + 112 + 132 + 152 + 1721 - 2
9693
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[SUSQOE10] Sums of Squares of TEN Consecutive Odd & Even Numbers
10 terms
F(x) ends with zero for all inputs - no palindromes exist!
up halt
[SUSQOE11] Sums of Squares of ELEVEN Consecutive Odd & Even Numbers
11 terms
Entry 1 by Kimberly Pellechi [ July 1, 2003 ]
Entry 4 by Hugo Sánchez [ March 17, 1999 ]
Odd entries between 3 to 27 by Kimberly Pellechi [ July 25, 2003 ]
Even entries up to 27 by Patrick De Geest [ July 25, 2023 ]
Entries 28 up to 83 by Patrick De Geest [ July 28, 2023 ]
83248.090.574.360.893.637.351.166.9662 + 248.090.574.360.893.637.351.166.9682 + … +
248.090.574.360.893.637.351.166.9842 + 248.090.574.360.893.637.351.166.9862		27
677.038.263.953.899.049.587.461.194.491.164.785.940.998.359.362.830.77654
82209.025.092.561.269.464.600.375.0882 + 209.025.092.561.269.464.600.375.0902 + … +
209.025.092.561.269.464.600.375.1062 + 209.025.092.561.269.464.600.375.1082		27
480.606.382.522.719.939.912.708.788.887.807.219.939.917.225.283.606.08454
81200.825.839.505.120.051.754.267.2822 + 200.825.839.505.120.051.754.267.2842 + … +
200.825.839.505.120.051.754.267.3002 + 200.825.839.505.120.051.754.267.3022		27
443.641.195.942.298.613.970.640.249.942.046.079.316.892.249.591.146.34454
8029.104.472.739.905.804.588.510.0932 + 29.104.472.739.905.804.588.510.0952 + … +
29.104.472.739.905.804.588.510.1112 + 29.104.472.739.905.804.588.510.1132		26
9.317.773.668.147.121.012.309.400.220.049.032.101.217.418.663.777.13952
7923.583.774.047.387.384.289.728.7442 + 23.583.774.047.387.384.289.728.7462 + … +
23.583.774.047.387.384.289.728.7622 + 23.583.774.047.387.384.289.728.7642		26
6.118.138.381.500.449.978.583.702.112.073.858.799.440.051.838.318.11652
7810.370.132.310.952.389.525.630.0592 + 10.370.132.310.952.389.525.630.0612 + … +
10.370.132.310.952.389.525.630.0772 + 10.370.132.310.952.389.525.630.0792		26
1.182.936.085.613.246.215.721.700.440.071.275.126.423.165.806.392.81152
77647.581.962.503.597.705.042.1122 + 647.581.962.503.597.705.042.1142 + … +
647.581.962.503.597.705.042.1302 + 647.581.962.503.597.705.042.1322		24
4.612.986.379.760.121.264.366.959.596.634.621.210.679.736.892.16449
76209.767.733.237.458.433.932.4882 + 209.767.733.237.458.433.932.4902 + … +
209.767.733.237.458.433.932.5062 + 209.767.733.237.458.433.932.5082		24
484.027.520.983.396.761.710.759.957.017.167.693.389.025.720.48448
75112.419.760.666.729.531.769.7812 + 112.419.760.666.729.531.769.7832 + … +
112.419.760.666.729.531.769.7992 + 112.419.760.666.729.531.769.8012		24
139.020.228.472.012.231.712.201.102.217.132.210.274.822.020.93148
7424.755.990.019.967.832.988.8162 + 24.755.990.019.967.832.988.8182 + … +
24.755.990.019.967.832.988.8342 + 24.755.990.019.967.832.988.8362		23
6.741.449.460.556.216.427.832.882.387.246.126.550.649.441.47646
739.425.558.973.509.620.207.9472 + 9.425.558.973.509.620.207.9492 + … +
9.425.558.973.509.620.207.9652 + 9.425.558.973.509.620.207.9672		22
977.252.781.594.184.979.148.343.841.979.481.495.187.252.77945
721.179.243.791.079.898.000.3912 + 1.179.243.791.079.898.000.3932 + … +
1.179.243.791.079.898.000.4092 + 1.179.243.791.079.898.000.4112		22
15.296.775.106.805.391.350.566.505.319.350.860.157.769.25144
7129.228.165.878.280.228.8932 + 29.228.165.878.280.228.8952 + … +
29.228.165.878.280.228.9112 + 29.228.165.878.280.228.9132		20
9.397.142.486.690.911.310.660.131.190.966.842.417.93940
7010.953.522.498.570.719.8492 + 10.953.522.498.570.719.8512 + … +
10.953.522.498.570.719.8672 + 10.953.522.498.570.719.8692		20
1.319.776.206.393.644.401.991.044.463.936.026.779.13140
697.839.138.448.896.382.6142 + 7.839.138.448.896.382.6162 + … +
7.839.138.448.896.382.6322 + 7.839.138.448.896.382.6342		19
675.973.007.830.621.420.575.024.126.038.700.379.57639
683.563.085.410.318.262.1992 + 3.563.085.410.318.262.2012 + … +
3.563.085.410.318.262.2172 + 3.563.085.410.318.262.2192		19
139.651.354.053.451.448.636.844.154.350.453.156.93139
672.169.502.789.486.731.2852 + 2.169.502.789.486.731.2872 + … +
2.169.502.789.486.731.3032 + 2.169.502.789.486.731.3052		19
51.774.165.889.497.791.577.519.779.498.856.147.71538
662.104.958.375.234.421.9422 + 2.104.958.375.234.421.9442 + … +
2.104.958.375.234.421.9602 + 2.104.958.375.234.421.9622		19
48.739.347.376.164.912.800.821.946.167.374.393.78438
65661.851.049.690.637.9382 + 661.851.049.690.637.9402 + … +
661.851.049.690.637.9562 + 661.851.049.690.637.9582		18
4.818.514.931.742.592.324.232.952.471.394.158.18437
64247.749.449.578.078.3662 + 247.749.449.578.078.3682 + … +
247.749.449.578.078.3842 + 247.749.449.578.078.3862		18
675.177.687.428.648.795.597.846.824.786.771.57636
63131.761.246.209.095.0692 + 131.761.246.209.095.0712 + … +
131.761.246.209.095.0872 + 131.761.246.209.095.0892		18
190.971.286.028.311.495.594.113.820.682.179.09136
62112.510.773.317.169.1992 + 112.510.773.317.169.2012 + … +
112.510.773.317.169.2172 + 112.510.773.317.169.2192		18
139.245.415.236.701.783.387.107.632.514.542.93136
6178.254.408.793.713.2142 + 78.254.408.793.713.2162 + … +
78.254.408.793.713.2322 + 78.254.408.793.713.2342		17
67.361.277.452.189.397.179.398.125.477.216.37635
6024.341.021.687.599.4562 + 24.341.021.687.599.4582 + … +
24.341.021.687.599.4742 + 24.341.021.687.599.4762		17
6.517.338.704.758.063.113.608.574.078.337.15634
5910.214.509.779.409.7592 + 10.214.509.779.409.7612 + … +
10.214.509.779.409.7772 + 10.214.509.779.409.7792		17
1.147.698.310.370.235.885.320.730.138.967.41134
583.720.028.131.419.3392 + 3.720.028.131.419.3412 + … +
3.720.028.131.419.3572 + 3.720.028.131.419.3592		16
152.224.702.284.064.666.460.482.207.422.25133
572.168.502.462.699.7852 + 2.168.502.462.699.7872 + … +
2.168.502.462.699.8032 + 2.168.502.462.699.8052		16
51.726.432.238.085.833.858.083.223.462.71532
561.118.164.120.751.5492 + 1.118.164.120.751.5512 + … +
1.118.164.120.751.5672 + 1.118.164.120.751.5692		16
13.753.201.010.297.177.179.201.010.235.73132
551.009.851.067.242.6092 + 1.009.851.067.242.6112 + … +
1.009.851.067.242.6272 + 1.009.851.067.242.6292		16
11.217.790.958.121.622.612.185.909.771.21132
54297.777.049.821.8972 + 297.777.049.821.8992 + … +
297.777.049.821.9152 + 297.777.049.821.9172		15
975.382.885.407.023.320.704.588.283.57930
53251.397.887.324.9762 + 251.397.887.324.9782 + … +
251.397.887.324.9942 + 251.397.887.324.9962		15
695.209.875.266.129.921.662.578.902.59630
52197.271.576.809.2022 + 197.271.576.809.2042 + … +
197.271.576.809.2202 + 197.271.576.809.2222		15
428.076.825.184.721.127.481.528.670.82430
5112.719.763.490.9792 + 12.719.763.490.9812 + … +
12.719.763.490.9972 + 12.719.763.490.9992		14
1.779.716.215.933.663.395.126.179.77128
5012.022.379.227.6912 + 12.022.379.227.6932 + … +
12.022.379.227.7092 + 12.022.379.227.7112		14
1.589.913.625.241.221.425.263.199.85128
4911.764.019.864.3392 + 11.764.019.864.3412 + … +
11.764.019.864.3572 + 11.764.019.864.3592		14
1.522.313.797.056.776.507.973.132.25128
484.187.614.073.4692 + 4.187.614.073.4712 + … +
4.187.614.073.4872 + 4.187.614.073.4892		13
192.897.227.912.393.219.722.798.29127
473.966.316.340.4292 + 3.966.316.340.4312 + … +
3.966.316.340.4472 + 3.966.316.340.4492		13
173.048.318.436.767.634.813.840.37127
463.280.806.257.8092 + 3.280.806.257.8112 + … +
3.280.806.257.8272 + 3.280.806.257.8292		13
118.400.586.714.787.417.685.004.81127
452.110.328.177.2382 + 2.110.328.177.2402 + … +
2.110.328.177.2562 + 2.110.328.177.2582		13
48.988.335.172.555.527.153.388.98426
44652.227.866.0122 + 652.227.866.0142 + … + 652.227.866.0302 + 652.227.866.032212
4.679.413.081.371.731.803.149.76425
43191.806.259.4082 + 191.806.259.4102 + … + 191.806.259.4262 + 191.806.259.428212
404.686.052.671.176.250.686.40424
42133.614.021.9612 + 133.614.021.9632 + … + 133.614.021.9792 + 133.614.021.981212
196.379.775.539.935.577.973.69124
4112.774.264.8792 + 12.774.264.8812 + … + 12.774.264.8972 + 12.774.264.899211
1.795.000.277.997.720.005.97122
4011.242.198.9492 + 11.242.198.9512 + … + 11.242.198.9672 + 11.242.198.969211
1.390.257.411.771.147.520.93122
396.203.358.9522 + 6.203.358.9542 + … + 6.203.358.9702 + 6.203.358.972210
423.298.286.525.682.892.32421
383.727.826.3392 + 3.727.826.3412 + … + 3.727.826.3572 + 3.727.826.359210
152.863.582.171.285.368.25121
372.948.906.1632 + 2.948.906.1652 + … + 2.948.906.1812 + 2.948.906.183210
95.656.523.788.732.565.65920
361.971.380.5522 + 1.971.380.5542 + … + 1.971.380.5702 + 1.971.380.572210
42.749.754.522.545.794.72420
351.111.454.8312 + 1.111.454.8332 + … + 1.111.454.8492 + 1.111.454.851210
13.588.650.499.405.688.53120
34379.083.1912 + 379.083.1932 + … + 379.083.2092 + 379.083.21129
1.580.744.806.084.470.85119
33301.314.8532 + 301.314.8552 + … + 301.314.8712 + 301.314.87329
998.697.113.311.796.89918
32235.998.7862 + 235.998.7882 + … + 235.998.8042 + 235.998.80629
612.649.748.847.946.21618
31200.249.9822 + 200.249.9842 + … + 200.250.0002 + 200.250.00229
441.100.652.256.001.14418
3024.356.4742 + 24.356.4762 + … + 24.356.4922 + 24.356.49428
6.525.621.441.265.25616
2913.371.5192 + 13.371.5212 + … + 13.371.5372 + 13.371.53928
1.966.775.665.776.69116
2811.846.4912 + 11.846.4932 + … + 11.846.5092 + 11.846.51128
1.543.735.445.373.45116
276.214.8782 + 6.214.8802 + … + 6.214.8962 + 6.214.89827
424.873.161.378.42415
264.228.4612 + 4.228.4632 + … + 4.228.4792 + 4.228.48127
196.679.636.976.69115
252.109.7422 + 2.109.7442 + … + 2.109.7602 + 2.109.76227
48.961.588.516.98414
241.011.1092 + 1.011.1112 + … + 1.011.1272 + 1.011.12927
11.245.977.954.21114
23424.6692 + 424.6712 + … + 424.6872 + 424.68926
1.983.874.783.89113
22124.9512 + 124.9532 + … + 124.9692 + 124.97126
171.767.767.17112
21119.0912 + 119.0932 + … + 119.1092 + 119.11126
156.035.530.65112
20101.1092 + 101.1112 + … + 101.1272 + 101.12926
112.475.574.21112
1942.4192 + 42.4212 + … + 42.4372 + 42.43925
19.802.420.89111
1813.1612 + 13.1632 + … + 13.1792 + 13.18125
1.908.228.09110
1711.0812 + 11.0832 + … + 11.0992 + 11.10125
1.353.113.53110
1610.1212 + 10.1232 + … + 10.1392 + 10.14125
1.129.009.21110
1510.1092 + 10.1112 + … + 10.1272 + 10.12925
1.126.336.21110
142.5042 + 2.5062 + 2.5082 + 2.5102 + 2.5122 + 2.5142 +
2.5162 + 2.5182 + 2.5202 + 2.5222 + 2.5242		4
69.522.5968
132.3962 + 2.3982 + 2.4002 + 2.4022 + 2.4042 + 2.4062 +
2.4082 + 2.4102 + 2.4122 + 2.4142 + 2.4162		4
63.677.6368
122.3842 + 2.3862 + 2.3882 + 2.3902 + 2.3922 + 2.3942 +
2.3962 + 2.3982 + 2.4002 + 2.4022 + 2.4042		4
63.044.0368
111.9522 + 1.9542 + 1.9562 + 1.9582 + 1.9602 + 1.9622 +
1.9642 + 1.9662 + 1.9682 + 1.9702 + 1.9722		4
42.344.3248
101.9082 + 1.9102 + 1.9122 + 1.9142 + 1.9162 + 1.9182 +
1.9202 + 1.9222 + 1.9242 + 1.9262 + 1.9282		4
40.466.4048
91.1912 + 1.1932 + 1.1952 + 1.1972 + 1.1992 + 1.2012 +
1.2032 + 1.2052 + 1.2072 + 1.2092 + 1.2112		4
15.866.8518
81.0092 + 1.0112 + 1.0132 + 1.0152 + 1.0172 + 1.0192 +
1.0212 + 1.0232 + 1.0252 + 1.0272 + 1.0292		4
11.422.4118
7992 + 1012 + 1032 + 1052 + 1072 + 1092 +
1112 + 1132 + 1152 + 1172 + 1192		2 - 3
131.1316
6522 + 542 + 562 + 582 + 602 + 622 +
642 + 662 + 682 + 702 + 722		2
42.7245
5292 + 312 + 332 + 352 + 372 + 392 +
412 + 432 + 452 + 472 + 492		2
17.1715
4212 + 232 + 252 + 272 + 292 + 312 +
332 + 352 + 372 + 392 + 412		2
11.0115
3142 + 162 + 182 + 202 + 222 + 242 +
262 + 282 + 302 + 322 + 342		2
6.7764
282 + 102 + 122 + 142 + 162 + 182 +
202 + 222 + 242 + 262 + 282		1 - 2
4.0044
112 + 32 + 52 + 72 + 92 + 112 +
132 + 152 + 172 + 192 + 212		1 - 2
1.7714



Contributions

Kimberly Pellechi (email) found many 'palindromic sums of the squares of the consecutive odd numbers'
or Pellechi Palindromes for short- go to topic 10.
 

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