Palindromic Sums of Squares of Consecutive Integers

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Palindromic Sums of Squares of Consecutive Integers
Sums of Odd/Even Squares Sums of Cubes Sums of Primes Sums of Powers Various Palindromic Sums

Introduction

Palindromic numbers are numbers which read the same from

left to right (forwards) as from the right to left (backwards)

Here are a few random examples : 535, 3773, 246191642

	Sums of Squares of TWO Consecutive Integers
	Sums of Squares of THREE Consecutive Integers
	Sums of Squares of FOUR Consecutive Integers
	Sums of Squares of FIVE Consecutive Integers
	Sums of Squares of SIX Consecutive Integers
	Sums of Squares of SEVEN Consecutive Integers
	Sums of Squares of EIGHT Consecutive Integers
	Sums of Squares of NINE Consecutive Integers
	Sums of Squares of TEN Consecutive Integers
	Sums of Squares of ELEVEN Consecutive Integers

PLAIN TEXT SUMSQUARE

Palindromic Sums of Squares

Case Sumsquare	Change of variables	CUDApalin parameters	Base Correction
2 terms	n.a.	A B C → 2 2 1	base = CUDAbase
3 terms	n.a.	A B C → 3 6 5	base = CUDAbase
4 terms	n.a.	A B C → 4 12 14	base = CUDAbase
5 terms	n.a.	A B C → 5 20 30	base = CUDAbase
6 terms	n.a.	A B C → 6 30 55	base = CUDAbase
7 terms	n.a.	A B C → 7 42 91	base = CUDAbase
8 terms	n.a.	A B C → 8 56 140	base = CUDAbase
9 terms	n.a.	A B C → 9 72 204	base = CUDAbase
10 terms	n.a.	A B C → 10 90 285	base = CUDAbase
11 terms	n.a.	A B C → 11 110 385	base = CUDAbase

The sequence for parameter 'A' is 2, 3, 4, 5, ... [+ 1]
The 'B' CUDApalin parameters are given by A002378 → Oblong (or promic, pronic, or heteromecic) numbers: a(n) = n*(n+1).
The 'C' CUDApalin parameters are given by A000330 → Square pyramidal numbers: a(n) = 0^2 + 1^2 + 2^2 + ... + n^2 = n*(n+1)*(2*n+1)/6.

Sums of TWO squared consecutives of the form 2*x^2 + 2*x + 1 can only start or end with a 1, 3 or 5.

1 can only be followed by an even number : 10, 12, 14, 16 or 18

3 can only be followed by 1 : 31

5 can only be followed by an even number : 50, 52, 54, 56 or 58

There are no palindromic sums of squares of type [SUSQ2] of EVEN lengths nor of ODD lengths 5, 9, 37, 39, 43.

Sums of THREE squared consecutives of the form 3*x^2 + 6*x + 5 can only start or end with a 0, 2, 4, 5, 7 or 9.

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 : 20

4 can only be followed by an odd number : 41, 43, 45, 47 or 49

5 can only be followed by an even number : 50, 52, 54, 56 or 58

7 can only be followed by a 7 : 77

9 can only be followed by an even number : 90, 92, 94, 96 or 98

There are no palindromic sums of squares of type [SUSQ3] of lengths 5, 8, 17, 24, 25, 26, 30, 32, 34, 36, 38, 41, 43, 46, 47, 49, 53.

Sums of FOUR squared consecutives of the form 4*x^2 + 12*x + 14 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 only be followed by an odd number : 41, 43, 45, 47 or 49

6 can only be followed by an even number : 60, 62, 64, 66 or 68

There are no palindromic sums of squares of type [SUSQ4] of EVEN lengths nor of ODD lengths 1, 3, 7, 11, 13, 21, 25, 33, 51.

Sums of FIVE squared consecutives of the form 5*x^2 + 20*x + 30 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 only be followed by an odd number : 51, 53, 55, 57 or 59

There are no palindromic sums of squares of type [SUSQ5] of lengths 1, 3, 4, 7, {10 up to 19}, 20, 21, 24, 25, 26, 30, 31, {33 up to 38}, 40, 41, 43, {45 up to 51}, 54, 55.

Sums of SIX squared consecutives of the form 6*x^2 + 30*x + 55 can only start or end with a 1, 5 or 9.

1 can only be followed by an odd number : 11, 13, 15, 17 or 19

5 can only be followed by 5 : 55

9 can only be followed by an odd number : 91, 93, 95, 97 or 99

There are no palindromic sums of squares of type [SUSQ6] of lengths 1, 3, 5, 7, 12, 14, 15, {17 up to 25}, 35, 36, 42, 43, 51.

Sums of SEVEN squared consecutives of the form 7*x^2 + 42*x + 91 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 0 : 30

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 2 : 82

There are no palindromic sums of squares of type [SUSQ7] of EVEN lengths nor of ODD lengths 1, {7 up to 13}, {19 up to 27}, 31, 39, 43, 47, 49.

Sums of EIGHT squared consecutives of the form 8*x^2 + 56*x + 140 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 9 : 29

4 can only be followed by an even number : 40, 42, 44, 46 or 48

There are no palindromic sums of squares of type [SUSQ8] of lengths {1 up to 4}, 6, 8, 10, 12, 14, 16, 18, 22, {24 up to 26}, 28, 30, 34, 38, 41, 42, 44, 46, {50 up to 52}, 54, 55.

Sums of NINE squared consecutives of the form 9*x^2 + 72*x + 204 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 8 : 58

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

There are no palindromic sums of squares of type [SUSQ9] of EVEN lengths nor of ODD lengths 1, 5, {13 up to 19}, 23, {39 up to 49}, 53.

Sums of TEN squared consecutives of the form 10*x^2 + 90*x + 285 can only start or end with a 5.

5 can only be followed by an even number : 50, 52, 54, 56 or 58

There are no palindromic sums of squares of type [SUSQ10] of lengths 1, 2, 4, 5 6, 8, 9, 10, {12 up to 16}, 19, 22, 23, {26 up to 30}, {33 up to 36}, 38, 40, 42, 45, 46, 48, 50, {52 up to 54}.

Sums of ELEVEN squared consecutives of the form 11*x^2 + 110*x + 385 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 odd number : 41, 43, 45, 47 or 49

5 can only be followed by 8 : 58

6 can only be followed by an even number : 60, 62, 64, 66 or 68

9 can only be followed by an even number : 90, 92, 94, 96 or 98

There are no palindromic sums of squares of type [SUSQ11] of lengths 1, 2, 3, 5, 9, 15, 19, 21, 29, 33, 35, 37, 41, 37, 44, 45, 47, 55.

A palindromic coincidence occurred with Five Consecutive Integers or is there a pattern ?

99 + 100 + 101 + 102 + 103 = 505
99² + 100² + 101² + 102² + 103² = 51015
10099 + 10100 + 10101 + 10102 + 10103 = 50505
10099² + 10100² + 10101² + 10102² + 10103² = 510151015

Two equations like 'number'-pregnancy. The children are the numbers 1981 and 699.

11² + 12² + 13² = 434
119811² + 119812² + 119813² = 43064746034

37² + 38² + 39² = 4334
36997² + 36998² + 36999² = 4106556014

Messages

[ August 1, 2005 ] Jean Claude Rosa (email) [ goto entry ]	Cher Patrick, voici les numéros 39 et 40 qui hélas ne sont pas premiers (le numéro 39 a 5 facteurs premiers mais le numéro 40 est un semi-prime -un "vrai"- avec un facteur de 15 chiffres et un autre de 17 chiffres ): numéro 39 : 1682059335368470748635339502861 = 29 * 109 * 35935429 * 206697457 * 71640539617 917076696729469² + 917076696729470² numéro 40: 3167016920841776771480296107613 = 113665666219493 * 27862564186498841 1258375325735882² + 1258375325735883² Voilà c'est tout pour les palindromes de la forme 1... ...1 ou 3... ...3 de 31 chiffres. J'ai commencé à chercher ceux de la forme 5... ...5 . Pour espérer trouver un palprime il faut donc s'attaquer aux nombres de 33 chiffres ( vraiment dur, dur ! ). A bientôt, JCR
[ September 6, 2005 ] Jean Claude Rosa (email) [ goto entry ]	Cher Patrick, voici le numéro 41 : 5450871426137276727316241780545 = 1650889370330016² + 1650889370330017² C'est le dernier des palindromes de 31 chiffres ! J'ai donc commencé la recherche des palindromes de 33 chiffres mais cela risque de prendre pas mal de temps... A bientôt. Kind regards. JCR
[ September 15, 2006 ] Jean Claude Rosa (email) [ goto entry ]	Cher Patrick, ca y est ! J'ai enfin trouvé le numéro 42. Le voici : 316370934175751979157571439073613 = 12577180410882082² + 12577180410882083² mais hélas il n'est pas premier (4 facteurs ) et comme j'ai fini l'étude des palindromes de la forme 31...13 pour trouver la cinquième solution du puzzle 14 il faudra étudier les nombres de 35 chiffres... Je ne sais pas si j'aurai le temps et le courage ! Je vais quand même essayer de finir l'étude des palindromes de 33 chiffres de la forme 5... ...5. JCR
[ October 14, 2006 ] Jean Claude Rosa (email) [ goto entry ]	Cher Patrick, ... et je viens de trouver le numéro 43. Le voici: 501263304966749757947669403362105 = 15831350305118476² + 15831350305118477² Voilà, c'est tout pour aujourd'hui... J'espère arriver un jour au numéro 50 ;-) JCR
[ May 21, 2007 ] Jean Claude Rosa (email) [ goto entry ]	Cher Patrick, Ca y est ! J'ai enfin trouvé le numéro 44. Le voici : 562318868215014101410512868813265 = 16767809460615511² + 16767809460615512² Amitiés. JCR
[ January 12, 2008 ] Jean Claude Rosa (email) [ goto entry ]	Cher Patrick, ... avec un peu de retard voici le numéro 45 : 588186547187469040964781745681885 = 17149147897016181² + 17149147897016182² Best regards. JCR
[ February 17, 2009 ] Jean Claude Rosa (email) [ goto entry ]	Cher Patrick, Voilà dejà un an que je n'ai pas eu de tes nouvelles ( le temps passe... ) mais j'attendais de trouver le numéro 46 pour t'écrire. Ca y est ! mais hélas il n'est pas premier (petite consolation c'est un semi-prime !). Le voici : 10489844562990321812309926544898401 = 2344709 * 4473836438974014179290447789 72421835667809200² + 72421835667809201² A bientôt. JCR

Sources Revealed

Huen Y.K. from Singapore developed a general generating function for palindromic sums and products
of consecutive integers using concise programcode written for Macsyma 2.2.1.
Global Generating Function For Palindromic Sums and Products of Consecutive Integers.

Neil Sloane's “Integer Sequences” Encyclopedia can be consulted online :

Neil Sloane's Integer Sequences

The regular numbers of form n² + (n+1)² [sums of two squared consecutives] :

%N Centered square numbers: 2n(n-1)+1. under A001844.

The subsets in relation to the palindromic and prime numbers of above form :

%N n^2 + (n+1)^2 is palindromic. under A027571.

%N Palindromes of form n^2 + (n+1)^2. under A027572.

%N n^2 + (n+1)^2 is prime. under A027861.

%N Primes of form n^2 + (n+1)^2. under A027862.

The regular numbers of form n² + (n+1)² + (n+2)² [sums of three squared consecutives] :

%N Points on surface of square pyramid: 3*n^2 + 2. under A005918.

The subsets in relation to the palindromic and prime numbers of above form :

%N n^2 + (n+1)^2 + (n+2)^2 is palindromic. under A027573.

%N Palindromes of form n^2 + (n+1)^2 + (n+2)^2. under A027574.

%N n^2 + (n+1)^2 + (n+2)^2 is prime. under A027863.

%N Primes of form n^2 + (n+1)^2 + (n+2)^2. under A027864.

The regular numbers of form n² + (n+1)² + (n+2)² + (n+3)² [sums of four squared consecutives] :

%N n^2 + (n+1)^2 + (n+2)^2 + (n+3)^2. under A027575.

The subsets in relation to the palindromic numbers of above form :

%N n^2 + (n+1)^2 + (n+2)^2 + (n+3)^2 is palindromic. under A027576.

%N Palindromes of form n^2 + (n+1)^2 + (n+2)^2 + (n+3)^2. under A027577.

The regular numbers of form n² + (n+1)² + (n+2)² + (n+3)² + (n+4)² [sums of five squared consecutives] :

%N n^2 + (n+1)^2 + (n+2)^2 + (n+3)^2 + (n+4)^2. under A027578.

The subsets in relation to the palindromic numbers of above form :

%N n^2 + (n+1)^2 + (n+2)^2 + (n+3)^2 + (n+4)^2 is palindromic. under A027579.

%N Palindromes of form n^2 + (n+1)^2 + (n+2)^2 + (n+3)^2 + (n+4)^2. under A027580.

The regular numbers of form n² + (n+1)² + (n+2)² + (n+3)² + (n+4)² + (n+5)² :

%N n^2 + (n+1)^2 + (n+2)^2 + (n+3)^2 + (n+4)^2 + (n+5)^2. under A027865.

The subsets in relation to the prime numbers of above form :

%N n^2 + (n+1)^2 + (n+2)^2 + (n+3)^2 + (n+4)^2 + (n+5)^2 is prime. under A027866.

%N Primes of form n^2 + (n+1)^2 + (n+2)^2 + (n+3)^2 + (n+4)^2 + (n+5)^2. under A027867.

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.

A simple substitution of n with (m–1) will proof that n^2 + (n+1)^2 + (n+2)^2 equals 3*n^2 + 2 :

n^2 + (n+1)^2 + (n+2)^2 =

(m–1)^2 + ((m–1)+1)^2 + ((m–1)+2)^2 =

(m^2–2m+1) + (m^2) + (m^2+2m+1) =

m^2 + 1 + m^2 + m^2 + 1 =

3*m^2 + 2 QED

And also that n^2 + (n+1)^2 equals 2n(n–1)+1 :

n^2 + (n+1)^2 =

(m–1)^2 + ((m–1)+1)^2 =

m^2–2m+1 + m^2 =

2m^2 – 2m + 1 =

2m(m–1) + 1 QED

The Table

Index Nr	Base Square Expression	Length
Index Nr	Palindromic Sums of Squares of Consecutive Integers	Length

	[SUSQ2] Sums of Squares of TWO Consecutive Integers Also [CP4] Palindromic Centered Squares (See my page Palindromic Centered Polygonals) Palindromes are of odd length only. A027571 & A027572 Carlos Rivera collects these palindromes (Palprimes and sums of powers) especially when they are prime (see highlights). Submissions from Jean Claude Rosa (email) Index 27 [ September 14, 2002 ] Index 28 [ October 11, 2002 ] Index 29, 30, 31 & 32 [ October 17, 18, 19 & 21, 2002 ] Index 33 [ February 10, 2003 ] Index 34 & 35 [ February 26, 2003 ] Index 36 & 37 [ June 8, 2005 ] Index 38 [ July 5, 2005 ] Index 39 & 40 [ August 1, 2005 ] Index 41 [ September 6, 2005 ] Index 42 [ September 15, 2006 ] Index 43 [ October 14, 2006 ] Index 44 [ May 21, 2007 ] Index 45 [ January 12, 2008 ] Index 46 [ February 17, 2009 ] Search resumed by Patrick De Geest Index 47 to 52 [ Last one June 16, 2021 ] Entries added by Robert Xiao Index 53 to 59 [ December 6, 2022 ] Entries added by Patrick De Geest Index 60 to 63 [ June 13, 2023 ] Entries added by Patrick De Geest Index 64 to 65 [ October 7, 2024 ]
No even-length palindromes exist!
65	16.818.129.062.880.276.245.974.449.686² + 16.818.129.062.880.276.245.974.449.687²	29
65	565.698.930.351.396.397.749.594.383.666.383.495.947.793.693.153.039.896.565	57
64	15.942.063.078.239.666.572.581.496.926² + 15.942.063.078.239.666.572.581.496.927²	29
64	508.298.750.381.144.786.639.244.037.323.730.442.936.687.441.183.057.892.805	57
63	1.262.413.288.821.833.950.379.107.737² + 1.262.413.288.821.833.950.379.107.738²	28
63	3.187.374.623.587.918.287.303.295.065.605.923.037.828.197.853.264.737.813	55
62	781.149.338.627.822.004.402.338.114² + 781.149.338.627.822.004.402.338.115²	27
62	1.220.388.578.477.367.461.271.198.953.598.911.721.647.637.748.758.830.221	55
61	722.342.892.165.927.171.629.878.924² + 722.342.892.165.927.171.629.878.925²	27
61	1.043.558.507.725.272.580.121.092.036.302.901.210.852.725.277.058.553.401	55
60	125.845.220.398.502.946.907.933.882² + 125.845.220.398.502.946.907.933.883²	27
60	31.674.038.994.295.564.414.718.234.143.281.741.446.559.249.983.047.613	53
59	12.485.050.866.969.785.154.347.907² + 12.485.050.866.969.785.154.347.908²	26
59	311.752.990.301.645.967.838.382.111.283.838.769.546.103.099.257.113	51
58	12.463.239.245.524.015.944.014.602² + 12.463.239.245.524.015.944.014.603²	26
58	310.664.664.982.340.084.364.343.252.343.463.480.043.289.466.466.013	51
57	9.137.327.500.983.204.356.513.194² + 9.137.327.500.983.204.356.513.195²	25
57	166.981.507.720.447.940.821.484.646.484.128.049.744.027.705.189.661	51
56	739.558.350.036.969.165.689.450² + 739.558.350.036.969.165.689.451²	24
56	1.093.893.106.218.808.420.715.399.935.170.248.088.126.013.983.901	49
55	79.608.488.039.503.229.466.585² + 79.608.488.039.503.229.466.586²	23
55	12.675.022.735.871.457.478.928.682.987.475.417.853.722.057.621	47
54	72.971.763.254.756.896.408.324² + 72.971.763.254.756.896.408.325²	23
54	10.649.756.465.016.577.599.097.379.099.577.561.056.465.794.601	47
53	9.057.485.682.660.759.666.330² + 9.057.485.682.660.759.666.331²	22
53	164.076.093.783.209.295.116.999.611.592.902.387.390.670.461	45
52	89.940.695.078.362.814.444² + 89.940.695.078.362.814.445²	20
52	16.178.657.262.358.073.985.458.937.085.326.275.687.161	41
51	84.753.839.053.503.067.854² + 84.753.839.053.503.067.855²	20
51	14.366.426.468.614.203.601.510.630.241.686.462.466.341	41
50	84.284.587.587.769.426.720² + 84.284.587.587.769.426.721²	20
50	14.207.783.409.680.752.220.402.225.708.690.438.770.241	41
49	124.566.258.570.164.697² + 124.566.258.570.164.698²	18
49	31.033.505.548.338.259.895.283.384.550.533.013	35
48	91.424.589.460.359.855² + 91.424.589.460.359.856²	17
48	16.716.911.115.990.684.748.609.951.111.961.761	35
47	89.663.751.709.213.505² + 89.663.751.709.213.506²	17
47	16.079.176.741.142.975.657.924.114.767.197.061	35
46	72.421.835.667.809.200² + 72.421.835.667.809.201²	17
46	10.489.844.562.990.321.812.309.926.544.898.401	35
45	17.149.147.897.016.181² + 17.149.147.897.016.182²	17
45	588.186.547.187.469.040.964.781.745.681.885	33
44	16.767.809.460.615.511² + 16.767.809.460.615.512²	17
44	562.318.868.215.014.101.410.512.868.813.265	33
43	15.831.350.305.118.476² + 15.831.350.305.118.477²	17
43	501.263.304.966.749.757.947.669.403.362.105	33
42	12.577.180.410.882.082² + 12.577.180.410.882.083²	17
42	316.370.934.175.751.979.157.571.439.073.613	33
41	1.650.889.370.330.016² + 1.650.889.370.330.017²	16
41	5.450.871.426.137.276.727.316.241.780.545	31
40	1.258.375.325.735.882² + 1.258.375.325.735.883²	16
40	3.167.016.920.841.776.771.480.296.107.613	31
39	917.076.696.729.469² + 917.076.696.729.470²	15
39	1.682.059.335.368.470.748.635.339.502.861	31
38	712.254.882.551.425² + 712.254.882.551.426²	15
38	1.014.614.035.436.689.866.345.304.164.101	31
37	86.505.526.088.570² + 86.505.526.088.571²	14
37	14.966.412.087.720.702.778.021.466.941	29
36	73.675.999.227.099² + 73.675.999.227.100²	14
36	10.856.305.724.223.132.242.750.365.801	29
35	12.615.243.893.562² + 12.615.243.893.563²	14
35	318.288.756.988.131.889.657.882.813	27
34	12.613.810.689.762² + 12.613.810.689.763²	14
34	318.216.440.234.333.432.044.612.813	27
33	7.365.154.696.775² + 7.365.154.696.776²	13
33	108.491.007.414.868.414.700.194.801	27
32	1.589.811.006.123² + 1.589.811.006.124²	13
32	5.054.998.070.382.830.708.994.505	25
31	1.258.837.943.717² + 1.258.837.943.718²	13
31	3.169.345.937.085.807.395.439.613	25
30	1.255.589.965.852² + 1.255.589.965.853²	13
30	3.153.012.324.698.964.232.103.513	25
29	1.250.999.800.012² + 1.250.999.800.013²	13
29	3.130.000.999.262.629.990.000.313	25
28	844.706.005.220² + 844.706.005.221²	12
28	1.427.056.470.511.150.746.507.241	25
27	165.058.650.666² + 165.058.650.667²	12
27	54.488.716.319.691.361.788.445	23
26	16.794.058.711² + 16.794.058.712²	11
26	564.080.816.010.618.080.465	21
25	12.574.461.617² + 12.574.461.618²	11
25	316.234.169.939.961.432.613	21
24	8.055.329.360² + 8.055.329.361²	10
24	129.776.662.212.266.677.921	21
23	8.032.814.139² + 8.032.814.140²	10
23	129.052.205.999.502.250.921	21
22	7.360.311.900² + 7.360.311.901²	10
22	108.348.382.545.283.843.801	21
21	1.705.387.643² + 1.705.387.644²	10
21	5.816.694.029.204.966.185	19
20	1.680.689.788² + 1.680.689.789²	10
20	5.649.436.330.336.349.465	19
19	1.616.689.803² + 1.616.689.804²	10
19	5.227.371.841.481.737.225	19
18	80.472.264² + 80.472.265²	8
18	12.951.570.707.515.921	17
17	17.070.706² + 17.070.707²	8
17	582.818.040.818.285	15
16	12.458.597² + 12.458.598²	8
16	310.433.303.334.013	15
15	8.659.929² + 8.659.930²	7
15	149.988.757.889.941	15
14	7.901.014² + 7.901.015²	7
14	124.852.060.258.421	15
13	1.258.182² + 1.258.183²	7
13	3.166.046.406.613	13
12	904.280² + 904.281²	6
12	1.635.446.445.361	13
11	170.706² + 170.707²	6
11	58.281.418.285	11
10	1.706² + 1.707²	4
10	5.824.285	7
9	1.621² + 1.622²	4
9	5.258.525	7
8	1.262² + 1.263²	4
8	Prime Curios! 3.187.813	7
7	1.257² + 1.258²	4
7	3.162.613	7
6	919² + 920²	3
6	1.690.961	7
5	16² + 17²	2
5	545	3
4	12² + 13²	2
4	Prime! 313	3
3	9² + 10²	1 - 2
3	Prime! 181	3
2	1² + 2²	1
2	Prime! 5	1
1	0² + 1²	1
1	1	1

	[SUSQ3] Sums of Squares of THREE Consecutive Integers Submissions from Jean Claude Rosa (email) Searched for palindromes up to length 21. A027573 & A027574 Index 23 and 24 [ August 28, 2002 ] Index 25 up to 29 [ August 30, 2002 ] Entries added by Robert Xiao Index 30 up to 47 [ November 13, 2022 ] Index 48 up to 54 [ December 6, 2022 ] Entries added by Patrick De Geest Index 55 up to 56 [ July 21, 2023 ]
56	1.173.218.266.644.871.938.456.265.897² + 1.173.218.266.644.871.938.456.265.898² + 1.173.218.266.644.871.938.456.265.899²	27
56	4.129.323.303.567.593.493.813.893.413.143.983.183.943.957.653.033.239.214	55
55	548.163.799.762.381.037.937.381.212² + 548.163.799.762.381.037.937.381.213² + 548.163.799.762.381.037.937.381.214²	27
55	901.450.654.109.795.320.991.582.599.995.285.199.023.597.901.456.054.109	54
54	40.527.845.339.124.306.034.326.041² + 40.527.845.339.124.306.034.326.042² + 40.527.845.339.124.306.034.326.043²	26
54	4.927.518.743.495.939.209.166.267.887.626.619.029.395.943.478.157.294	52
53	26.015.490.337.146.521.135.930.989² + 26.015.490.337.146.521.135.930.990² + 26.015.490.337.146.521.135.930.991²	26
53	2.030.417.212.446.492.035.882.938.008.392.885.302.946.442.127.140.302	52
52	25.959.833.459.686.661.892.013.519² + 25.959.833.459.686.661.892.013.520² + 25.959.833.459.686.661.892.013.521²	26
52	2.021.738.859.764.001.484.200.291.441.920.024.841.004.679.588.371.202	52
51	13.680.321.023.122.374.054.395.688² + 13.680.321.023.122.374.054.395.689² + 13.680.321.023.122.374.054.395.690²	26
51	561.453.549.887.051.997.681.159.464.951.186.799.150.788.945.354.165	51
50	2.582.535.036.965.557.492.159.599² + 2.582.535.036.965.557.492.159.600² + 2.582.535.036.965.557.492.159.601²	25
50	20.008.461.651.464.080.207.443.677.634.470.208.046.415.616.480.002	50
49	407.064.532.506.683.719.135.791² + 407.064.532.506.683.719.135.792² + 407.064.532.506.683.719.135.793²	24
49	497.104.600.874.654.898.782.368.863.287.898.456.478.006.401.794	48
48	8.340.484.531.860.307.902.839² + 8.340.484.531.860.307.902.840² + 8.340.484.531.860.307.902.841²	22
48	208.691.046.678.603.178.418.424.814.871.306.876.640.196.802	45
47	4.100.752.341.022.460.813.848² + 4.100.752.341.022.460.813.849² + 4.100.752.341.022.460.813.850²	22
47	50.448.509.287.203.578.252.833.825.287.530.278.290.584.405	44
46	258.199.039.883.824.087.999² + 258.199.039.883.824.088.000² + 258.199.039.883.824.088.001²	21
46	200.000.232.590.785.746.343.343.647.587.095.232.000.002	42
45	37.944.021.248.974.850.861² + 37.944.021.248.974.850.862² + 37.944.021.248.974.850.863²	20
45	4.319.246.245.627.965.003.443.005.697.265.426.429.134	40
44	12.887.330.239.769.396.341² + 12.887.330.239.769.396.342² + 12.887.330.239.769.396.343²	20
44	498.249.842.126.624.179.828.971.426.621.248.942.894	39
43	831.985.816.181.113.329² + 831.985.816.181.113.330² + 831.985.816.181.113.331²	18
43	2.076.601.194.979.659.897.989.569.794.911.066.702	37
42	179.711.480.947.862.766² + 179.711.480.947.862.767² + 179.711.480.947.862.768²	18
42	96.888.649.153.422.126.862.122.435.194.688.869	35
41	129.218.991.085.740.250² + 129.218.991.085.740.251² + 129.218.991.085.740.252²	18
41	50.092.642.971.649.855.355.894.617.924.629.005	35
40	116.914.306.830.157.497² + 116.914.306.830.157.498² + 116.914.306.830.157.499²	18
40	41.006.865.424.728.636.563.682.742.456.860.014	35
39	13.468.617.939.580.690² + 13.468.617.939.580.691² + 13.468.617.939.580.692²	17
39	544.211.007.607.184.454.481.706.700.112.445	33
38	1.609.332.492.201.364² + 1.609.332.492.201.365² + 1.609.332.492.201.366²	16
38	7.769.853.211.365.169.615.631.123.589.677	31
37	128.895.228.580.157² + 128.895.228.580.158² + 128.895.228.580.159²	15
37	49.841.939.852.193.539.125.893.914.894	29
36	122.759.320.720.921² + 122.759.320.720.922² + 122.759.320.720.923²	15
36	45.209.552.471.586.568.517.425.590.254	29
35	83.405.649.337.159² + 83.405.649.337.160² + 83.405.649.337.161²	14
35	20.869.507.024.059.895.042.070.596.802	29
34	82.170.676.118.779² + 82.170.676.118.780² + 82.170.676.118.781²	14
34	20.256.060.041.452.325.414.006.065.202	29
33	39.587.830.255.967² + 39.587.830.255.968² + 39.587.830.255.969²	14
33	4.701.588.913.126.006.213.198.851.074	28
32	12.360.779.113.221² + 12.360.779.113.222² + 12.360.779.113.223²	14
32	458.366.580.857.595.758.085.663.854	27
31	129.426.069.200² + 129.426.069.201² + 129.426.069.202²	12
31	50.253.322.166.466.122.335.205	23
30	37.196.982.751² + 37.196.982.752² + 37.196.982.753²	11
30	4.150.846.577.557.756.480.514	22
29	17.552.348.196² + 17.552.348.197² + 17.552.348.198²	11
29	924.254.781.686.187.452.429	21
28	16.028.474.344² + 16.028.474.345² + 16.028.474.346²	11
28	770.735.969.484.969.537.077	21
27	12.900.321.391² + 12.900.321.392² + 12.900.321.393²	11
27	499.254.876.050.678.452.994	21
26	8.227.749.489² + 8.227.749.490² + 8.227.749.491²	10
26	203.087.585.010.585.780.302	21
25	5.602.945.242² + 5.602.945.243² + 5.602.945.244²	10
25	94.178.986.188.168.987.149	20
24	828.223.249² + 828.223.250² + 828.223.251²	9
24	2.057.861.255.521.687.502	19
23	441.564.380² + 441.564.381² + 441.564.382²	9
23	584.937.307.703.739.485	18
22	40.439.557² + 40.439.558² + 40.439.559²	8
22	4.906.073.553.706.094	16
21	17.909.282² + 17.909.283² + 17.909.284²	8
21	962.227.252.722.269	15
20	8.211.879² + 8.211.880² + 8.211.881²	7
20	202.304.919.403.202	15
19	4.427.780² + 4.427.781² + 4.427.782²	7
19	58.815.733.751.885	14
18	1.775.706² + 1.775.707² + 1.775.708²	7
18	9.459.406.049.549	13
17	1.751.496² + 1.751.497² + 1.751.498²	7
17	Prime Curios! 9.203.225.223.029	13
16	1.328.120² + 1.328.121² + 1.328.122²	7
16	5.291.716.171.925	13
15	378.811² + 378.812² + 378.813²	6
15	430.495.594.034	12
14	173.736² + 173.737² + 173.738²	6
14	90.553.635.509	11
13	119.811² + 119.812² + 119.813²	6
13	43.064.746.034	11
12	40.441² + 40.442² + 40.443²	5
12	4.906.666.094	10
11	36.997² + 36.998² + 36.999²	5
11	4.106.556.014	10
10	17.932² + 17.933² + 17.934²	5
10	964.777.469	9
9	17.552² + 17.553² + 17.554²	5
9	924.323.429	9
8	16.084² + 16.085² + 16.086²	5
8	776.181.677	9
7	8.339² + 8.340² + 8.341²	4
7	208.666.802	9
6	1.736² + 1.737² + 1.738²	4
6	9.051.509	7
5	566² + 567² + 568²	3
5	964.469	6
4	37² + 38² + 39²	2
4	4.334	4
3	11² + 12² + 13²	2
3	434	3
2	4² + 5² + 6²	1
2	77	2
1	0² + 1² + 2²	1
1	Prime! 5	1

	[SUSQ4] Sums of Squares of FOUR Consecutive Integers (Palindromes are of odd-length only) [PDG] Searched up to length 17. A027576 & A027577 Entries from Donovan Johnson (OEIS) Index 7 & 8 [ August 26, 2012 ] Entries from Chai Wah Wu (OEIS) Index 9 & 10 [ September 6, 2021 ] Entries added by Robert Xiao Index 11 up to 22 [ November 13, 2022 ] Index 23 up to 27 [ December 6, 2022 ] Entries added by Patrick De Geest Index 28 up to 30 [ July 21, 2023 ]
No even-length palindromes exist!
30	1.304.158.980.962.924.998.650.981.369² + 1.304.158.980.962.924.998.650.981.370² + 1.304.158.980.962.924.998.650.981.371² + 1.304.158.980.962.924.998.650.981.372²	28
30	6.803.322.590.505.019.876.166.220.133.310.226.616.789.105.050.952.233.086	55
29	1.085.305.943.350.996.169.800.705.742² + 1.085.305.943.350.996.169.800.705.743² + 1.085.305.943.350.996.169.800.705.744² + 1.085.305.943.350.996.169.800.705.745²	28
29	4.711.555.962.691.982.828.932.337.796.977.332.398.282.891.962.695.551.174	55
28	106.543.267.346.550.117.365.047.427² + 106.543.267.346.550.117.365.047.428² + 106.543.267.346.550.117.365.047.429² + 106.543.267.346.550.117.365.047.430²	27
28	45.405.871.267.513.809.946.832.612.521.623.864.990.831.576.217.850.454	53
27	1.272.871.463.910.655.112.869.984² + 1.272.871.463.910.655.112.869.985² + 1.272.871.463.910.655.112.869.986² + 1.272.871.463.910.655.112.869.987²	25
27	6.480.807.054.552.216.725.775.159.515.775.276.122.554.507.080.846	49
26	1.090.625.222.702.062.964.649.330² + 1.090.625.222.702.062.964.649.331² + 1.090.625.222.702.062.964.649.332² + 1.090.625.222.702.062.964.649.333²	25
26	4.757.853.505.575.697.751.400.812.180.041.577.965.755.053.587.574	49
25	1.063.249.088.931.509.259.171.027² + 1.063.249.088.931.509.259.171.028² + 1.063.249.088.931.509.259.171.029² + 1.063.249.088.931.509.259.171.030²	25
25	4.521.994.500.454.737.941.688.051.508.861.497.374.540.054.991.254	49
24	126.542.779.266.073.782.044.963² + 126.542.779.266.073.782.044.964² + 126.542.779.266.073.782.044.965² + 126.542.779.266.073.782.044.966²	24
24	64.052.299.937.529.090.675.261.916.257.609.092.573.999.225.046	47
23	12.289.864.995.068.396.717.849² + 12.289.864.995.068.396.717.850² + 12.289.864.995.068.396.717.851² + 12.289.864.995.068.396.717.852²	23
23	604.163.126.388.030.091.527.888.725.190.030.883.621.361.406	45
22	1.107.721.851.419.374.353.357² + 1.107.721.851.419.374.353.358² + 1.107.721.851.419.374.353.359² + 1.107.721.851.419.374.353.360²	22
22	4.908.190.800.447.865.884.417.144.885.687.440.080.918.094	43
21	1.063.803.884.153.944.534.777² + 1.063.803.884.153.944.534.778² + 1.063.803.884.153.944.534.779² + 1.063.803.884.153.944.534.780²	22
21	4.526.714.815.764.076.176.238.326.716.704.675.184.176.254	43
20	109.526.531.972.273.658.717² + 109.526.531.972.273.658.718² + 109.526.531.972.273.658.719² + 109.526.531.972.273.658.720²	21
20	47.984.244.823.493.935.958.185.953.939.432.844.248.974	41
19	12.657.045.958.221.760.784² + 12.657.045.958.221.760.785² + 12.657.045.958.221.760.786² + 12.657.045.958.221.760.787²	20
19	640.803.249.554.151.242.686.242.151.455.942.308.046	39
18	1.085.552.783.348.274.742² + 1.085.552.783.348.274.743² + 1.085.552.783.348.274.744² + 1.085.552.783.348.274.745²	19
18	4.713.699.381.740.745.292.925.470.471.839.963.174	37
17	111.378.861.419.824.307² + 111.378.861.419.824.308² + 111.378.861.419.824.309² + 111.378.861.419.824.310²	18
17	49.621.003.084.705.711.111.750.748.030.012.694	35
16	1.304.322.969.770.628² + 1.304.322.969.770.629² + 1.304.322.969.770.630² + 1.304.322.969.770.631²	16
16	6.805.033.637.885.097.905.887.363.305.086	31
15	1.252.515.421.951.968² + 1.252.515.421.951.969² + 1.252.515.421.951.970² + 1.252.515.421.951.971²	16
15	6.275.179.528.910.080.800.198.259.715.726	31
14	1.107.745.868.127.265² + 1.107.745.868.127.266² + 1.107.745.868.127.267² + 1.107.745.868.127.268²	16
14	4.908.403.633.412.125.212.143.363.048.094	31
13	131.203.548.945.928² + 131.203.548.945.929² + 131.203.548.945.930² + 131.203.548.945.931²	15
13	68.857.485.024.027.672.042.058.475.886	29
12	102049984166197² + 102.049.984.166.198² + 102.049.984.166.199² + 102.049.984.166.200²	15
12	41.656.797.073.285.458.237.079.765.614	29
11	12.881.503.131.739² + 12.881.503.131.740² + 12.881.503.131.741² + 12.881.503.131.742²	14
11	663.732.491.732.161.237.194.237.366	27
10	109.244.416.317² + 109.244.416.318² + 109.244.416.319² + 109.244.416.320²	12
10	47.737.369.987.078.996.373.774	23
9	107.045.858.977² + 107.045.858.978² + 107.045.858.979² + 107.045.858.980²	12
9	45.835.263.697.779.636.253.854	23
8	1.086.219.242² + 1.086.219.243² + 1.086.219.244² + 1.086.219.245²	10
8	4.719.488.979.798.849.174	19
7	1.085.864.492² + 1.085.864.493² + 1.085.864.494² + 1.085.864.495²	10
7	4.716.406.792.976.046.174	19
6	102.025.300² + 102.025.301² + 102.025.302² + 102.025.303²	9
6	41.636.648.584.663.614	17
5	101.740.172² + 101.740.173² + 101.740.174² + 101.740.175²	9
5	41.404.251.615.240.414	17
4	12.309.598² + 12.309.599² + 12.309.600² + 12.309.601²	8
4	606.104.959.401.606	15
3	10.460.137² + 10.460.138² + 10.460.139² + 10.460.140²	8
3	437.657.989.756.734	15
2	10.172² + 10.173² + 10.174² + 10.175²	5
2	414.000.414	9
1	100² + 101² + 102² + 103²	3
1	41.214	5

	[SUSQ5] Sums of Squares of FIVE Consecutive Integers [PDG] Searched up to length 17. A027579 & A027580 Entry from Chai Wah Wu (OEIS) Index 6 [ January 18, 2016 ] Entry from Giovanni Resta (OEIS) Index 7 [ August 04, 2019 ] Entries added by Robert Xiao Index 8 up to 14 [ November 13, 2022 ] Index 15 [ December 6, 2022 ] Entries added by Patrick De Geest Index 16 [ July 21, 2023 ]
16	103.111.501.282.578.599.285.032.343² + 103.111.501.282.578.599.285.032.344² + 103.111.501.282.578.599.285.032.345² + 103.111.501.282.578.599.285.032.346² + 103.111.501.282.578.599.285.032.347²	27
16	53.159.908.483.736.040.626.825.443.134.452.862.604.063.738.480.995.135	53
15	33.427.767.483.384.295.424.777.661² + 33.427.767.483.384.295.424.777.662² + 33.427.767.483.384.295.424.777.663² + 33.427.767.483.384.295.424.777.664² + 33.427.767.483.384.295.424.777.665²	26
15	5.587.078.194.616.022.157.488.222.772.228.847.512.206.164.918.707.855	52
14	3.214.369.116.793.269.645.387² + 3.214.369.116.793.269.645.388² + 3.214.369.116.793.269.645.389² + 3.214.369.116.793.269.645.390² + 3.214.369.116.793.269.645.391²	22
14	51.660.844.094.971.721.771.133.117.712.717.949.044.806.615	44
13	320.203.534.322.536.731.169² + 320.203.534.322.536.731.170² + 320.203.534.322.536.731.171² + 320.203.534.322.536.731.172² + 320.203.534.322.536.731.173²	21
13	512.651.516.963.219.792.177.771.297.912.369.615.156.215	42
12	10.530.595.917.944.837.331² + 10.530.595.917.944.837.332² + 10.530.595.917.944.837.333² + 10.530.595.917.944.837.334² + 10.530.595.917.944.837.335²	20
12	554.467.251.935.182.356.060.653.281.539.152.764.455	39
11	10.105.796.967.151.826.397² + 10.105.796.967.151.826.398² + 10.105.796.967.151.826.399² + 10.105.796.967.151.826.400² + 10.105.796.967.151.826.401²	20
11	510.635.661.706.475.263.070.362.574.607.166.536.015	39
10	3.342.595.144.302.035² + 3.342.595.144.302.036² + 3.342.595.144.302.037² + 3.342.595.144.302.038² + 3.342.595.144.302.039²	16
10	55.864.711.493.557.777.775.539.411.746.855	32
9	104.883.758.798.995² + 104.883.758.798.996² + 104.883.758.798.997² + 104.883.758.798.998² + 104.883.758.798.999²	15
9	55.003.014.299.030.903.099.241.030.055	29
8	32.195.622.174.079² + 32.195.622.174.080² + 32.195.622.174.081² + 32.195.622.174.082² + 32.195.622.174.083²	14
8	5.182.790.435.880.880.885.340.972.815	28
7	10.310.949.321.253² + 10.310.949.321.254² + 10.310.949.321.255² + 10.310.949.321.256² + 10.310.949.321.257²	14
7	531.578.379.527.444.725.973.875.135	27
6	105.720.053.635² + 105.720.053.636² + 105.720.053.637² + 105.720.053.638² + 105.720.053.639²	12
6	55.883.648.705.050.784.638.855	23
5	10.099² + 10.100² + 10.101² + 10.102² + 10.103²	5
5	510.151.015	9
4	3.207² + 3.208² + 3.209² + 3.210² + 3.211²	4
4	51.488.415	8
3	331² + 332² + 333² + 334² + 335²	3
3	554.455	6
2	99² + 100² + 101² + 102² + 103²	2 - 3
2	51.015	5
1	1² + 2² + 3² + 4² + 5²	1
1	55	2

	[SUSQ6] Sums of Squares of SIX Consecutive Integers Entries added by Patrick De Geest Index 1 up to 28 [ June 30, 2023 ] Index 29 up to 49 [ July 21, 2023 ]
49	1.246.756.851.350.801.868.238.455.343² + 1.246.756.851.350.801.868.238.455.344² + … + 1.246.756.851.350.801.868.238.455.347² + 1.246.756.851.350.801.868.238.455.348²	28
49	9.326.415.878.340.992.797.577.093.748.473.907.757.972.990.438.785.146.239	55
48	542.222.359.810.800.474.662.640.191² + 542.222.359.810.800.474.662.640.192² + … + 542.222.359.810.800.474.662.640.195² + 542.222.359.810.800.474.662.640.196²	27
48	1.764.030.524.872.759.042.543.142.396.932.413.452.409.572.784.250.304.671	55
47	170.907.263.094.476.310.290.694.641² + 170.907.263.094.476.310.290.694.642² + … + 170.907.263.094.476.310.290.694.645² + 170.907.263.094.476.310.290.694.646²	27
47	175.255.755.470.667.265.375.010.909.909.010.573.562.766.074.557.552.571	54
46	160.826.196.650.501.385.090.782.431² + 160.826.196.650.501.385.090.782.432² + … + 160.826.196.650.501.385.090.782.435² + 160.826.196.650.501.385.090.782.436²	27
46	155.190.393.174.394.457.621.492.153.351.294.126.754.493.471.393.091.551	54
45	48.259.273.696.946.117.904.370.946² + 48.259.273.696.946.117.904.370.947² + … + 48.259.273.696.946.117.904.370.950² + 48.259.273.696.946.117.904.370.951²	26
45	13.973.744.986.540.532.557.250.053.535.005.275.523.504.568.944.737.931	53
44	15.842.486.038.008.463.370.046.681² + 15.842.486.038.008.463.370.046.682² + … + 15.842.486.038.008.463.370.046.685² + 15.842.486.038.008.463.370.046.686²	26
44	1.505.906.183.186.958.594.525.588.558.855.254.958.596.813.816.095.051	52
43	13.694.092.462.684.948.770.528.809² + 13.694.092.462.684.948.770.528.810² + … + 13.694.092.462.684.948.770.528.813² + 13.694.092.462.684.948.770.528.814²	26
43	1.125.169.010.259.388.350.211.072.112.701.120.538.839.520.109.615.211	52
42	3.029.371.063.184.185.019.896.200² + 3.029.371.063.184.185.019.896.201² + … + 3.029.371.063.184.185.019.896.204² + 3.029.371.063.184.185.019.896.205²	25
42	55.062.534.230.746.077.048.343.166.134.384.077.064.703.243.526.055	50
41	571.077.148.488.056.628.936.119² + 571.077.148.488.056.628.936.120² + … + 571.077.148.488.056.628.936.123² + 571.077.148.488.056.628.936.124²	24
41	1.956.774.657.151.499.278.013.210.123.108.729.941.517.564.776.591	49
40	304.203.348.018.855.275.515.250² + 304.203.348.018.855.275.515.251² + … + 304.203.348.018.855.275.515.254² + 304.203.348.018.855.275.515.255²	24
40	555.238.061.675.284.679.272.559.955.272.976.482.576.160.832.555	48
39	180.149.574.473.124.882.100.294² + 180.149.574.473.124.882.100.295² + … + 180.149.574.473.124.882.100.298² + 180.149.574.473.124.882.100.299²	24
39	194.723.215.097.087.808.853.106.601.358.808.780.790.512.327.491	48
38	57.636.490.290.250.267.440.451² + 57.636.490.290.250.267.440.452² + … + 57.636.490.290.250.267.440.455² + 57.636.490.290.250.267.440.456²	23
38	19.931.790.077.868.680.147.419.591.474.108.686.877.009.713.991	47
37	39.019.978.639.441.536.466.923² + 39.019.978.639.441.536.466.924² + … + 39.019.978.639.441.536.466.927² + 39.019.978.639.441.536.466.928²	23
37	9.135.352.398.134.842.676.020.440.206.762.484.318.932.535.319	46
36	38.954.405.131.787.489.403.373² + 38.954.405.131.787.489.403.374² + … + 38.954.405.131.787.489.403.377² + 38.954.405.131.787.489.403.378²	23
36	9.104.674.075.028.588.938.035.225.308.398.858.205.704.764.019	46
35	16.130.526.716.044.422.304.981² + 16.130.526.716.044.422.304.982² + … + 16.130.526.716.044.422.304.985² + 16.130.526.716.044.422.304.986²	23
35	1.561.163.352.822.137.130.063.883.600.317.312.282.533.611.651	46
34	5.020.014.970.134.500.237.731² + 5.020.014.970.134.500.237.732² + … + 5.020.014.970.134.500.237.735² + 5.020.014.970.134.500.237.736²	22
34	151.203.301.802.246.923.882.797.288.329.642.208.103.302.151	45
33	1.524.865.239.807.802.834.321² + 1.524.865.239.807.802.834.322² + … + 1.524.865.239.807.802.834.325² + 1.524.865.239.807.802.834.326²	22
33	13.951.283.997.444.648.274.222.247.284.644.479.938.215.931	44
32	96.518.362.998.060.917.055² + 96.518.362.998.060.917.056² + … + 96.518.362.998.060.917.059² + 96.518.362.998.060.917.060²	20
32	55.894.766.374.952.728.664.046.682.725.947.366.749.855	41
31	48.133.889.267.562.677.549² + 48.133.889.267.562.677.550² + … + 48.133.889.267.562.677.553² + 48.133.889.267.562.677.554²	20
31	13.901.227.776.131.913.091.219.031.913.167.772.210.931	41
30	16.059.122.247.918.927.881² + 16.059.122.247.918.927.882² + … + 16.059.122.247.918.927.885² + 16.059.122.247.918.927.886²	20
30	1.547.372.444.241.628.076.666.708.261.424.442.737.451	40
29	15.904.195.857.857.829.764² + 15.904.195.857.857.829.765² + … + 15.904.195.857.857.829.768² + 15.904.195.857.857.829.769²	20
29	1.517.660.675.310.612.898.118.982.160.135.760.667.151	40
28	9.601.949.622.120.202.530² + 9.601.949.622.120.202.531² + … + 9.601.949.622.120.202.534² + 9.601.949.622.120.202.535²	19
28	553.184.619.274.405.801.242.108.504.472.916.481.355	39
27	4.452.442.039.733.210.509² + 4.452.442.039.733.210.510² + … + 4.452.442.039.733.210.513² + 4.452.442.039.733.210.514²	19
27	118.945.440.703.101.792.787.297.101.307.044.549.811	39
26	4.382.301.630.150.914.711² + 4.382.301.630.150.914.712² + … + 4.382.301.630.150.914.715² + 4.382.301.630.150.914.716²	19
26	115.227.405.465.740.186.939.681.047.564.504.722.511	39
25	3.049.949.111.805.146.980² + 3.049.949.111.805.146.981² + … + 3.049.949.111.805.146.984² + 3.049.949.111.805.146.985²	19
25	55.813.137.507.606.029.811.892.060.670.573.131.855	38
24	1.250.952.385.197.428.052² + 1.250.952.385.197.428.053² + … + 1.250.952.385.197.428.056² + 1.250.952.385.197.428.057²	19
24	9.389.291.220.186.806.497.946.086.810.221.929.839	37
23	573.719.286.716.525.976² + 573.719.286.716.525.977² + … + 573.719.286.716.525.980² + 573.719.286.716.525.981²	18
23	1.974.922.919.703.116.052.506.113.079.192.294.791	37
22	30.395.024.110.760.260² + 30.395.024.110.760.261² + … + 30.395.024.110.760.264² + 30.395.024.110.760.265²	17
22	5.543.144.944.162.186.116.812.614.494.413.455	34
21	4.369.937.734.757.661² + 4.369.937.734.757.662² + … + 4.369.937.734.757.665² + 4.369.937.734.757.666²	16
21	114.578.134.833.953.636.359.338.431.875.411	33
20	4.028.463.491.342.037² + 4.028.463.491.342.038² + … + 4.028.463.491.342.041² + 4.028.463.491.342.042²	16
20	97.371.108.606.454.166.145.460.680.117.379	32
19	477.815.505.424.671² + 477.815.505.424.672² + … + 477.815.505.424.675² + 477.815.505.424.676²	15
19	1.369.845.943.345.417.145.433.495.489.631	31
18	182.044.518.133.594² + 182.044.518.133.595² + … + 182.044.518.133.598² + 182.044.518.133.599²	15
18	198.841.239.494.960.069.494.932.148.891	30
17	127.596.868.866.987² + 127.596.868.866.988² + … + 127.596.868.866.991² + 127.596.868.866.992²	15
17	97.685.765.667.958.285.976.656.758.679	29
16	39.437.797.541.318² + 39.437.797.541.319² + … + 39.437.797.541.322² + 39.437.797.541.323²	14
16	9.332.039.249.461.111.649.429.302.339	28
15	12.751.697.307.158² + 12.751.697.307.159² + … + 12.751.697.307.162² + 12.751.697.307.163²	14
15	975.634.705.280.666.082.507.436.579	27
14	1.363.323.900.136² + 1.363.323.900.137² + … + 1.363.323.900.140² + 1.363.323.900.141²	13
14	11.151.912.340.133.104.321.915.111	26
13	40.350.112² + 40.350.113² + 40.350.114² + 40.350.115² + 40.350.116² + 40.350.117²	8
13	9.768.790.440.978.679	16
12	962.270² + 962.271² + 962.272² + 962.273² + 962.274² + 962.275²	6
12	5.555.810.185.555	13
11	542.179² + 542.180² + 542.181² + 542.182² + 542.183² + 542.184²	6
11	1.763.764.673.671	13
10	96.005² + 96.006² + 96.007² + 96.008² + 96.009² + 96.010²	5
10	55.304.640.355	11
9	54.191² + 54.192² + 54.193² + 54.194² + 5.4195² + 54.196²	5
9	17.621.612.671	11
8	30.300² + 30.301² + 30.302² + 30.303² + 30.304² + 30.305²	5
8	5.509.449.055	10
7	5.626² + 5.627² + 5.628² + 5.629² + 5.630² + 5.631²	4
7	Prime! 190.080.091	9
6	3.988² + 3.989² + 3.990² + 3.991² + 3.992² + 3.993²	4
6	95.544.559	8
5	1.359² + 1.360² + 1.361² + 1.362² + 1.363² + 1.364²	4
5	11.122.111	8
4	176² + 177² + 178² + 179² + 180² + 181²	3
4	191.191	6
3	149² + 150² + 151² + 152² + 153² + 154²	3
3	137.731	6
2	11² + 12² + 13² + 14² + 15² + 16²	2
2	1.111	4
1	0² + 1² + 2² + 3² + 4² + 5²	1
1	55	2

	[SUSQ7] Sums of Squares of SEVEN Consecutive Integers Entries added by Patrick De Geest Index 1 up to 9 [ July 1, 2023 ] Index 10 up to 16 [ July 21, 2023 ]
No even-length palindromes exist!
16	407.875.788.882.303.226.699.821.284² + 407.875.788.882.303.226.699.821.285² + … + 407.875.788.882.303.226.699.821.289² + 407.875.788.882.303.226.699.821.290²	27
16	1.164.538.614.094.528.347.281.064.343.434.601.827.438.254.904.168.354.611	55
15	52.941.577.951.010.701.978.916.050² + 52.941.577.951.010.701.978.916.051² + … + 52.941.577.951.010.701.978.916.055² + 52.941.577.951.010.701.978.916.056²	26
15	19.619.674.731.600.597.623.921.199.299.112.932.679.500.613.747.691.691	53
14	39.808.561.111.314.872.834.977.084² + 39.808.561.111.314.872.834.977.085² + … + 39.808.561.111.314.872.834.977.089² + 39.808.561.111.314.872.834.977.090²	26
14	11.093.050.764.273.035.763.155.002.620.055.136.753.037.246.705.039.011	53
13	4.121.502.285.926.871.883.067.684² + 4.121.502.285.926.871.883.067.685² + … + 4.121.502.285.926.871.883.067.689² + 4.121.502.285.926.871.883.067.690²	25
13	118.907.467.650.303.012.756.533.787.335.657.210.303.056.764.709.811	51
12	9.665.310.835.617.236.491.849² + 9.665.310.835.617.236.491.850² + … + 9.665.310.835.617.236.491.854² + 9.665.310.835.617.236.491.855²	22
12	653.927.634.843.699.736.312.030.213.637.996.348.436.729.356	45
11	4.761.660.494.316.531.312.864² + 4.761.660.494.316.531.312.865² + … + 4.761.660.494.316.531.312.869² + 4.761.660.494.316.531.312.870²	22
11	158.713.874.641.943.273.318.999.813.372.349.146.478.317.851	45
10	43.992.211.425.744.948.574² + 43.992.211.425.744.948.575² + … + 43.992.211.425.744.948.579² + 43.992.211.425.744.948.580²	20
10	13.547.202.662.892.110.808.580.801.129.826.620.274.531	41
9	500.518.060.847.751.590² + 500.518.060.847.751.591² + … + 500.518.060.847.751.595² + 500.518.060.847.751.596²	18
9	1.753.628.304.643.554.962.694.553.464.038.263.571	37
8	40.835.962.570.960.210² + 40.835.962.570.960.211² + … + 40.835.962.570.960.215² + 40.835.962.570.960.216²	17
8	11.673.030.873.678.044.144.087.637.803.037.611	35
7	8.893.946.160.332.178² + 8.893.946.160.332.179² + … + 8.893.946.160.332.183² + 8.893.946.160.332.184²	16
7	553.715.948.120.212.818.212.021.849.517.355	33
6	65.701.105.596.692² + 65.701.105.596.693² + … + 65.701.105.596.697² + 65.701.105.596.698²	14
6	30.216.446.936.396.469.363.964.461.203	29
5	40.113.478.132.484² + 40.113.478.132.485² + … + 40.113.478.132.489² + 40.113.478.132.490²	14
5	11.263.637.895.198.589.159.873.636.211	29
4	46.305.230² + 46.305.231² + 46.305.232² + … + 46.305.234² + 46.305.235² + 46.305.236²	8
4	15.009.222.222.290.051	17
3	10.841.357² + 10.841.358² + 10.841.359² + … + 10.841.361² + 10.841.362² + 10.841.363²	8
3	822.745.606.547.228	15
2	50² + 51² + 52² + 53² + 54² + 55² + 56²	2
2	19.691	5
1	6² + 7² + 8² + 9² + 10² + 11² + 12²	1 - 2
1	595	3

	[SUSQ8] Sums of Squares of EIGHT Consecutive Integers Entries added by Patrick De Geest Index 1 up to 36 [ July 2, 2023 ] Index 37 up to 45 [ July 21, 2023 ]
45	72.925.716.519.393.087.527.409.582² + 72.925.716.519.393.087.527.409.583² + … + 72.925.716.519.393.087.527.409.588² + 72.925.716.519.393.087.527.409.589²	26
45	42.545.281.038.935.054.852.345.653.335.654.325.845.053.983.018.254.524	53
44	71.292.233.851.896.013.469.376.201² + 71.292.233.851.896.013.469.376.202² + … + 71.292.233.851.896.013.469.376.207² + 71.292.233.851.896.013.469.376.208²	26
44	40.660.660.860.747.423.150.293.049.894.039.205.132.474.706.806.606.604	53
43	759.406.297.947.692.779.080.037² + 759.406.297.947.692.779.080.038² + … + 759.406.297.947.692.779.080.043² + 759.406.297.947.692.779.080.044²	24
43	4.613.583.402.900.959.504.061.974.791.604.059.590.092.043.853.164	49
42	709.051.284.960.270.620.443.367² + 709.051.284.960.270.620.443.368² + … + 709.051.284.960.270.620.443.373² + 709.051.284.960.270.620.443.374²	24
42	4.022.029.797.630.487.117.982.533.352.897.117.840.367.979.202.204	49
41	606.731.587.061.101.323.087.914² + 606.731.587.061.101.323.087.915² + … + 606.731.587.061.101.323.087.920² + 606.731.587.061.101.323.087.921²	24
41	2.944.985.749.901.462.195.628.777.778.265.912.641.099.475.894.492	49
40	234.633.282.074.423.957.471.996² + 234.633.282.074.423.957.471.997² + … + 234.633.282.074.423.957.472.002² + 234.633.282.074.423.957.472.003²	24
40	440.422.216.456.129.590.461.650.056.164.095.921.654.612.224.044	48
39	77.471.834.906.927.642.830.352² + 77.471.834.906.927.642.830.353² + … + 77.471.834.906.927.642.830.358² + 77.471.834.906.927.642.830.359²	23
39	48.015.081.630.770.019.305.975.457.950.391.007.703.618.051.084	47
38	6.029.567.265.159.967.012.419² + 6.029.567.265.159.967.012.420² + … + 6.029.567.265.159.967.012.425² + 6.029.567.265.159.967.012.426²	22
38	290.845.451.240.709.151.585.525.585.151.907.042.154.548.092	45
37	604.323.528.288.194.201.784² + 604.323.528.288.194.201.785² + … + 604.323.528.288.194.201.790² + 604.323.528.288.194.201.791²	21
37	2.921.655.414.741.534.861.038.301.684.351.474.145.561.292	43
36	24.498.027.310.345.048.391² + 24.498.027.310.345.048.392² + … + 24.498.027.310.345.048.397² + 24.498.027.310.345.048.398²	20
36	4.801.226.736.787.294.768.668.674.927.876.376.221.084	40
35	7.454.999.550.045.000.446² + 7.454.999.550.045.000.447² + … + 7.454.999.550.045.000.450² + 7.454.999.550.045.000.451²	19
35	444.616.146.329.369.273.292.372.963.923.641.616.444	39
34	7.439.022.276.072.654.647² + 7.439.022.276.072.654.648² + … + 7.439.022.276.072.654.653² + 7.439.022.276.072.654.654²	19
34	442.712.419.391.241.434.424.434.142.193.914.217.244	39
33	745.500.450.004.499.547² + 745.500.450.004.499.548² + … + 745.500.450.004.499.553² + 745.500.450.004.499.554²	18
33	4.446.167.367.655.290.670.760.925.567.637.616.444	37
32	742.326.018.579.714.122² + 742.326.018.579.714.123² + … + 742.326.018.579.714.128² + 742.326.018.579.714.129²	18
32	4.408.383.342.883.280.648.460.823.882.433.838.044	37
31	725997492049303282² + 725997492049303283² + … + 725997492049303288² + 725.997.492.049.303.289²	18
31	4.216.578.867.695.025.497.945.205.967.688.756.124	37
30	245.526.151.053.791.616² + 245.526.151.053.791.617² + … + 245.526.151.053.791.622² + 245.526.151.053.791.623²	18
30	482.264.726.810.314.396.693.413.018.627.462.284	36
29	76.581.332.942.288.106² + 76.581.332.942.288.107² + … + 76.581.332.942.288.112² + 76.581.332.942.288.113²	17
29	46.917.604.441.740.655.955.604.714.440.671.964	35
28	60.299.210.677.888.324² + 60.299.210.677.888.325² + … + 60.299.210.677.888.330² + 60.299.210.677.888.331²	17
28	29.087.958.467.010.893.539.801.076.485.978.092	35
27	7.485.678.803.902.771² + 7.485.678.803.902.772² + … + 7.485.678.803.902.777² + 7.485.678.803.902.778²	16
27	448.283.097.241.594.181.495.142.790.382.844	33
26	6.068.491.431.508.564² + 6.068.491.431.508.565² + … + 6.068.491.431.508.570² + 6.068.491.431.508.571²	16
26	294.612.706.034.343.222.343.430.607.216.492	33
25	6.021.813.714.533.369² + 6.021.813.714.533.370² + … + 6.021.813.714.533.375² + 6.021.813.714.533.376²	16
25	290.097.923.300.337.707.733.003.329.790.092	33
24	2.450.294.139.073.766² + 2.450.294.139.073.767² + … + 2.450.294.139.073.770² + 2.450.294.139.073.771²	16
24	48.031.530.943.834.122.143.834.903.513.084	32
23	2.311.832.320.635.482² + 2.311.832.320.635.483² + … + 2.311.832.320.635.488² + 2.311.832.320.635.489²	16
23	42.756.549.429.878.833.887.892.494.565.724	32
22	1.904.699.668.432.799² + 1.904.699.668.432.800² + … + 1.904.699.668.432.805² + 1.904.699.668.432.806²	16
22	29.023.046.615.424.222.242.451.664.032.092	32
21	1.904.665.004.560.194² + 1.904.665.004.560.195² + … + 1.904.665.004.560.200² + 1.904.665.004.560.201²	16
21	29.021.990.236.770.377.307.763.209.912.092	32
20	760.971.445.026.431² + 760.971.445.026.431² + … + 760.971.445.026.431² + 760.971.445.026.431²	15
20	4.632.620.321.164.958.594.611.230.262.364	31
19	745.499.954.999.547² + 745.499.954.999.548² + … + 745.499.954.999.553² + 745.499.954.999.554²	15
19	4.446.161.463.234.654.564.323.641.616.444	31
18	70.963.996.389.626² + 70.963.996.389.627² + … + 70.963.996.389.632² + 70.963.996.389.633²	14
18	40.287.110.268.698.789.686.201.178.204	29
17	7.642.076.368.506² + 7.642.076.368.507² + … + 7.642.076.368.512² + 7.642.076.368.513²	13
17	467.210.649.777.050.777.946.012.764	27
16	7.455.004.499.547² + 7.455.004.499.548² + … + 7.455.004.499.553² + 7.455.004.499.554²	13
16	444.616.736.706.545.607.637.616.444	27
15	7.259.484.959.532² + 7.259.484.959.533² + … + 7.259.484.959.538² + 7.259.484.959.539²	13
15	421.600.975.021.777.120.579.006.124	27
14	6.066.499.582.454² + 6.066.499.582.455² + … + 6.066.499.582.460² + 6.066.499.582.461²	13
14	294.419.337.471.656.174.733.914.492	27
13	76.252.089.781² + 76.252.089.782² + … + 76.252.089.787² + 76.252.089.788²	11
13	46.515.049.572.027.594.051.564	23
12	60.707.103.529² + 60.707.103.530² + … + 60.707.103.535² + 60.707.103.536²	11
12	29.482.819.354.445.391.828.492	23
11	7.454.999.547² + 7.454.999.548² + … + 7.454.999.553² + 7.454.999.554²	10
11	444.616.146.383.641.616.444	21
10	1.917.875.604² + 1.917.875.605² + … + 1.917.875.612² + 1.917.875.613²	10
10	29.425.974.766.747.952.492	20
9	745.500.446² + 745.500.447² + … + 745.500.452² + 745.500.453²	9
9	4.446.167.361.637.616.444	19
8	602.986.044² + 602.986.045² + … + 602.986.050² + 602.986.051²	9
8	2.908.737.387.837.378.092	19
7	74.549.547² + 74.549.548² + … + 74.549.553² + 74.549.554²	8
7	44.461.083.838.016.444	17
6	7.628.212² + 7.628.213² + … + 7.628.218² + 7.628.219²	7
6	465.517.373.715.564	15
5	602.299² + 602.300² + 602.301² + 602.302² + 602.303² + 602.304² + 602.305² + 602.306²	6
5	2.902.146.412.092	13
4	60.639² + 60.640² + 60.641² + 60.642² + 60.643² + 60.644² + 60.645² + 60.646²	5
4	29.420.102.492	11
3	6.024² + 6.025² + 6.026² + 6.027² + 6.028² + 6.029² + 6.030² + 6.031²	4
3	290.646.092	9
2	599² + 600² + 601² + 602² + 603² + 604² + 605² + 606²	3
2	2.904.092	7
1	71² + 72² + 73² + 74² + 75² + 76² + 77² + 78²	2
1	44.444	5

	[SUSQ9] Sums of Squares of NINE Consecutive Integers Entries added by Patrick De Geest Index 1 up to 14 [ July 3, 2023 ] Index 15 and 16 [ July 21, 2023 ]
No even-length palindromes exist!
16	1.024.046.790.546.298.685.965.662.657² + 1.024.046.790.546.298.685.965.662.658² + … + 1.024.046.790.546.298.685.965.662.664² + 1.024.046.790.546.298.685.965.662.665²	28
16	9.438.046.463.053.574.386.084.368.456.548.634.806.834.753.503.646.408.349	55
15	8.418.418.922.408.859.014.078.654² + 8.418.418.922.408.859.014.078.655² + … + 8.418.418.922.408.859.014.078.661² + 8.418.418.922.408.859.014.078.662²	25
15	637.827.994.378.543.815.047.405.191.504.740.518.345.873.499.728.736	51
14	706.842.547.278.119.370² + 706.842.547.278.119.371² + … + 706.842.547.278.119.377² + 706.842.547.278.119.378²	18
14	4.496.637.479.783.583.802.083.853.879.747.366.944	37
13	37.252.579.423.357.573² + 37.252.579.423.357.574² + … + 37.252.579.423.357.580² + 37.252.579.423.357.581²	17
13	12.489.792.063.242.079.097.024.236.029.798.421	35
12	8.804.185.700.033.448² + 8.804.185.700.033.449² + … + 8.804.185.700.033.455² + 8.804.185.700.033.456²	16
12	697.623.172.566.061.727.160.665.271.326.796	33
11	8.069.410.711.476.471² + 8.069.410.711.476.472² + … + 8.069.410.711.476.488² + 8.069.410.711.476.489²	16
11	586.038.503.074.421.434.124.470.305.830.685	33
10	1.034.142.517.618.595² + 1.034.142.517.618.596² + … + 1.034.142.517.618.602² + 1.034.142.517.618.603²	16
10	9.625.056.720.718.809.088.170.276.505.269	31
9	42.706.771.441.429² + 42.706.771.441.430² + … + 42.706.771.441.436² + 42.706.771.441.437²	14
9	16.414.814.942.557.175.524.941.841.461	29
8	6.910.770.803.932² + 6.910.770.803.933² + … + 6.910.770.803.939² + 6.910.770.803.940²	13
8	429.828.777.940.808.049.777.828.924	27
7	1.015.600.243.367² + 1.015.600.243.368² + … + 10.156.002.433.74² + 1.015.600.243.375²	13
7	9.282.994.689.017.109.864.992.829	25
6	7.058.602.172² + 7.058.602.173² + … + 7.058.602.179² + 7.058.602.180²	10
6	448.414.782.111.287.414.844	21
5	68.982² + 68.983² + 68.984² + 68.985² + 68.986² + 68.987² + 68.988² + 68.989² + 68.990²	5
5	42.831.613.824	11
4	36.869² + 36.870² + 36.871² + 36.872² + 36.873² + 36.874² + 3.6875² + 36.876² + 36.877²	5
4	12.236.563.221	11
3	8.274² + 8.275² + 8.276² + 8.277² + 8.278² + 8.279² + 8.280² + 8.281² + 8.282²	4
3	616.727.616	9
2	864² + 865² + 866² + 867² + 868² + 869² + 870² + 871² + 872²	3
2	6.780.876	7
1	4⁵ + 5² + 6² + 7² + 8² + 9² + 10² + 11² + 12²	1 - 2
1	636	3

	[SUSQ10] Sums of Squares of TEN Consecutive Integers Entries added by Patrick De Geest Index 1 up to 16 [ July 4, 2023 ] Index 17 up to 28 [ July 22, 2023 ]
28	762.822.192.941.087.387.594.324.285² + 762.822.192.941.087.387.594.324.286² + … + 762.822.192.941.087.387.594.324.293² + 762.822.192.941.087.387.594.324.294²	27
28	5.818.976.980.434.495.526.221.575.936.395.751.226.255.944.340.896.798.185	55
27	708.238.332.735.419.802.345.068.322² + 708.238.332.735.419.802.345.068.323² + … + 708.238.332.735.419.802.345.068.330² + 708.238.332.735.419.802.345.068.331²	27
27	5.016.015.359.558.472.128.061.240.456.540.421.608.212.748.559.535.106.105	55
26	707.360.277.029.636.941.970.263.864² + 707.360.277.029.636.941.970.263.865² + … + 707.360.277.029.636.941.970.263.872² + 707.360.277.029.636.941.970.263.873²	27
26	5.003.585.615.194.447.199.639.158.998.998.519.369.917.444.915.165.853.005	55
25	7.094.286.358.335.770.548.368.662² + 7.094.286.358.335.770.548.368.663² + … + 7.094.286.358.335.770.548.368.670² + 7.094.286.358.335.770.548.368.671²	25
25	503.288.989.340.690.090.055.327.616.723.550.090.096.043.989.882.305	51
24	739.091.386.598.511.305.912.548² + 739.091.386.598.511.305.912.549² + … + 739.091.386.598.511.305.912.556² + 739.091.386.598.511.305.912.557²	24
24	5.462.560.777.441.100.976.053.726.273.506.790.011.447.770.652.645	49
23	76.427.669.665.074.490.053.911² + 76.427.669.665.074.490.053.912² + … + 76.427.669.665.074.490.053.919² + 76.427.669.665.074.490.053.920²	23
23	58.411.886.904.337.474.146.929.692.964.147.473.340.968.811.485	47
22	71.109.714.639.962.026.018.789² + 71.109.714.639.962.026.018.790² + … + 71.109.714.639.962.026.018.797² + 71.109.714.639.962.026.018.798²	23
22	50.565.915.161.768.296.916.653.235.661.969.286.716.151.956.505	47
21	2.413.975.059.180.116.670.316² + 2.413.975.059.180.116.670.317² + … + 2.413.975.059.180.116.670.324² + 2.413.975.059.180.116.670.325²	22
21	58.272.755.863.436.477.807.600.670.877.463.436.855.727.285	44
20	712.880.958.612.545.587.687² + 712.880.958.612.545.587.688² + … + 712.880.958.612.545.587.695² + 712.880.958.612.545.587.696²	21
20	5.081.992.611.523.419.351.195.911.539.143.251.162.991.805	43
19	710.922.401.190.724.500.314² + 710.922.401.190.724.500.315² + … + 710.922.401.190.724.500.322² + 710.922.401.190.724.500.323²	21
19	5.054.106.605.147.854.404.282.824.044.587.415.066.014.505	43
18	707.648.582.582.913.973.927² + 707.648.582.582.913.973.928² + … + 707.648.582.582.913.973.935² + 707.648.582.582.913.973.936²	21
18	5.007.665.164.316.072.185.010.105.812.706.134.615.667.005	43
17	76.784.840.135.287.606.361² + 76.784.840.135.287.606.362² + … + 76.784.840.135.287.606.369² + 76.784.840.135.287.606.370²	20
17	58.959.116.746.016.744.358.185.344.761.064.761.195.985	41
16	7.673.059.342.909.318.615² + 7.673.059.342.909.318.616² + … + 7.673.059.342.909.318.623² + 7.673.059.342.909.318.624²	19
16	588.758.396.798.079.844.212.448.970.897.693.857.885	39
15	714.069.089.116.909.234² + 714.069.089.116.909.235² + … + 714.069.089.116.909.242² + 714.069.089.116.909.243²	18
15	5.098.946.640.322.524.678.764.252.230.466.498.905	37
14	2.256.983.914.610.382² + 2.256.983.914.610.383² + … + 2.256.983.914.610.390² + 2.256.983.914.610.391²	16
14	50.939.763.908.100.244.200.180.936.793.905	32
13	735.586.816.803.598² + 735.586.816.803.599² + … + 735.586.816.803.606² + 735.586.816.803.607²	15
13	5.410.879.650.552.566.652.550.569.780.145	31
12	711.631.203.385.272² + 711.631.203.385.273² + … + 711.631.203.385.280² + 711.631.203.385.281²	15
12	5.064.189.696.315.767.675.136.969.814.605	31
11	764.141.248.965² + 764.141.248.966² + … + 764.141.248.973² + 764.141.248.974²	12
11	5.839.118.483.766.673.848.119.385	25
10	242.496.951.676² + 242.496.951.677² + … + 242.496.951.684² + 242.496.951.685²	12
10	588.047.715.743.347.517.740.885	24
9	7.099.786.684² + 7.099.786.685² + … + 7.099.786.692² + 7.099.786.693²	10
9	504.069.710.222.017.960.405	21
8	2.419.367.721² + 2.419.367.722² + … + 2.419.367.729² + 2.419.367.730²	10
8	58.533.401.911.910.433.585	20
7	225.541.812² + 225.541.813² + … + 225.541.820² + 225.541.821²	9
7	508.691.109.901.196.805	18
6	73.940.223² + 73.940.224² + 73.940.225² + … + 73.940.230² + 73.940.231² + 73.940.232²	8
6	54.671.572.427.517.645	17
5	73.909.868² + 73.909.869² + 73.909.870² + … + 73.909.875² + 73.909.876² + 73.909.877²	8
5	54.626.692.529.662.645	17
4	73.891.988² + 73.891.989² + 73.891.990² + … + 73.891.995² + 73.891.996² + 73.891.997²	8
4	54.600.265.556.200.645	17
3	76.625² + 76.626² + 76.627² + … + 76.632² + 76.633² + 76.634²	5
3	58.720.802.785	11
2	709² + 710² + 711² + 712² + 713² + 714² + 715² + 716² + 717² + 718²	3
2	5.090.905	7
1	2² + 3² + 4² + 5² + 6² + 7² + 8² + 9² + 10² + 11²	1 - 2
1	505	3

	[SUSQ11] Sums of Squares of ELEVEN Consecutive Integers Entries added by Patrick De Geest Index 1 up to 61 [ July 6, 2023 ] Index 62 up to 83 [ July 22, 2023 ]
83	114.677.948.655.448.469.830.307.506² + 114.677.948.655.448.469.830.307.507² + … + 114.677.948.655.448.469.830.307.515² + 114.677.948.655.448.469.830.307.516²	27
83	144.661.350.986.038.430.603.090.281.182.090.306.034.830.689.053.166.441	54
82	112.983.682.309.587.573.794.843.434² + 112.983.682.309.587.573.794.843.435² + … + 112.983.682.309.587.573.794.843.443² + 112.983.682.309.587.573.794.843.444²	27
82	140.418.437.150.571.932.807.627.860.068.726.708.239.175.051.734.814.041	54
81	41.364.417.751.789.101.975.882.126² + 41.364.417.751.789.101.975.882.127² + … + 41.364.417.751.789.101.975.882.135² + 41.364.417.751.789.101.975.882.136²	26
81	18.821.165.615.389.779.241.145.465.356.454.114.297.798.351.656.112.881	53
80	23.813.568.461.128.461.633.742.211² + 23.813.568.461.128.461.633.742.212² + … + 23.813.568.461.128.461.633.742.220² + 23.813.568.461.128.461.633.742.221²	26
80	6.237.946.471.381.373.851.745.289.229.825.471.583.731.831.746.497.326	52
79	23.066.112.406.098.030.496.016.260² + 23.066.112.406.098.030.496.016.261² + … + 23.066.112.406.098.030.496.016.269² + 23.066.112.406.098.030.496.016.270²	26
79	5.852.500.956.838.244.210.883.301.991.033.880.124.428.386.590.052.585	52
78	12.274.620.024.520.540.750.511.066² + 12.274.620.024.520.540.750.511.067² + … + 12.274.620.024.520.540.750.511.075² + 12.274.620.024.520.540.750.511.076²	26
78	1.657.329.264.209.967.044.568.666.556.668.654.407.699.024.629.237.561	52
77	7.540.412.625.643.349.969.781.679² + 7.540.412.625.643.349.969.781.680² + … + 7.540.412.625.643.349.969.781.688² + 7.540.412.625.643.349.969.781.689²	25
77	625.436.048.214.578.030.037.126.818.621.730.030.875.412.840.634.526	51
76	2.486.610.538.095.367.452.060.891² + 2.486.610.538.095.367.452.060.892² + … + 2.486.610.538.095.367.452.060.900² + 2.486.610.538.095.367.452.060.901²	25
76	68.015.551.649.836.261.532.190.388.309.123.516.263.894.615.551.086	50
75	1.295.358.655.580.359.510.523.564² + 1.295.358.655.580.359.510.523.565² + … + 1.295.358.655.580.359.510.523.573² + 1.295.358.655.580.359.510.523.574²	25
75	18.457.494.512.456.521.008.006.899.860.080.012.565.421.549.475.481	50
74	1.075.353.482.862.788.584.567.046² + 1.075.353.482.862.788.584.567.047² + … + 1.075.353.482.862.788.584.567.055² + 1.075.353.482.862.788.584.567.056²	25
74	12.720.236.244.156.427.162.357.100.175.326.172.465.144.263.202.721	50
73	1.052.698.005.579.718.016.122.244² + 1.052.698.005.579.718.016.122.245² + … + 1.052.698.005.579.718.016.122.253² + 1.052.698.005.579.718.016.122.254²	25
73	12.189.904.000.466.676.257.454.688.645.475.267.666.400.040.998.121	50
72	915.056.418.612.690.783.108.022² + 915.056.418.612.690.783.108.023² + … + 915.056.418.612.690.783.108.031² + 915.056.418.612.690.783.108.032²	24
72	9.210.610.741.687.123.901.443.104.013.441.093.217.861.470.160.129	49
71	199.521.799.695.417.304.977.523² + 199.521.799.695.417.304.977.524² + … + 199.521.799.695.417.304.977.532² + 199.521.799.695.417.304.977.533²	24
71	437.898.434.090.680.474.706.314.413.607.474.086.090.434.898.734	48
70	194.467.104.346.151.551.657.537² + 194.467.104.346.151.551.657.538² + … + 194.467.104.346.151.551.657.546² + 194.467.104.346.151.551.657.547²	24
70	415.992.001.400.546.952.828.898.898.828.259.645.004.100.299.514	48
69	11.600.670.342.086.993.685.706² + 11.600.670.342.086.993.685.707² + … + 11.600.670.342.086.993.685.715² + 11.600.670.342.086.993.685.716²	23
69	1.480.331.076.243.544.438.138.998.318.344.453.426.701.330.841	46
68	755.099.986.980.000.055.579² + 755.099.986.980.000.055.580² + … + 755.099.986.980.000.055.588² + 755.099.986.980.000.055.589²	21
68	6.271.935.893.709.158.788.096.908.878.519.073.985.391.726	43
67	409.618.484.944.105.728.564² + 409.618.484.944.105.728.565² + … + 409.618.484.944.105.728.573² + 409.618.484.944.105.728.574²	21
67	1.845.660.335.286.950.285.791.975.820.596.825.330.665.481	43
66	203.854.057.497.947.626.397² + 203.854.057.497.947.626.398² + … + 203.854.057.497.947.626.406² + 203.854.057.497.947.626.407²	21
66	457.121.244.342.141.905.669.966.509.141.243.442.121.754	42
65	97.642.351.896.275.280.054² + 97.642.351.896.275.280.055² + … + 97.642.351.896.275.280.063² + 97.642.351.896.275.280.064²	20
65	104.874.317.722.196.580.575.575.085.691.227.713.478.401	42
64	23.373.374.598.588.045.739² + 23.373.374.598.588.045.740² + … + 23.373.374.598.588.045.748² + 23.373.374.598.588.045.749²	20
64	6.009.461.041.385.129.773.663.779.215.831.401.649.006	40
63	12.276.010.268.353.331.066² + 12.276.010.268.353.331.067² + … + 12.276.010.268.353.331.075² + 12.276.010.268.353.331.076²	20
63	1.657.704.709.195.880.658.888.560.885.919.074.077.561	40
62	11.470.873.693.487.491.984² + 11.470.873.693.487.491.985² + … + 11.470.873.693.487.491.993² + 11.470.873.693.487.491.994²	20
62	1.447.390.376.211.377.139.449.317.731.126.730.937.441	40
61	7.394.694.548.491.960.189² + 7.394.694.548.491.960.190² + … + 7.394.694.548.491.960.198² + 7.394.694.548.491.960.199²	19
61	601.496.582.120.463.865.363.568.364.021.285.694.106	39
60	2.424.492.985.667.531.071² + 2.424.492.985.667.531.072² + … + 2.424.492.985.667.531.080² + 2.424.492.985.667.531.081²	19
60	64.659.828.613.061.649.522.594.616.031.682.895.646	38
59	2.307.472.718.272.536.810² + 2.307.472.718.272.536.811² + … + 2.307.472.718.272.536.819² + 2.307.472.718.272.536.820²	19
59	58.568.733.801.292.550.600.605.529.210.833.786.585	38
58	2.071.167.316.361.978.263² + 2.071.167.316.361.978.264² + … + 2071.167.316.361.978.272² + 2.071.167.316.361.978.273²	19
58	47.187.074.576.026.868.688.686.862.067.547.078.174	38
57	245.620.073.137.586.031² + 245.620.073.137.586.032² + … + 245.620.073.137.586.040² + 245.620.073.137.586.041²	18
57	663.621.423.609.244.247.742.442.906.324.126.366	36
56	239.175.801.864.662.479² + 239.175.801.864.662.480² + … + 239.175.801.864.662.488² + 239.175.801.864.662.489²	18
56	629.255.706.173.647.147.741.746.371.607.552.926	36
55	194.068.619.876.058.387² + 194.068.619.876.058.388² + … + 194.068.619.876.058.396² + 194.068.619.876.058.397²	18
55	414.288.921.426.578.510.015.875.624.129.882.414	36
54	116.220.651.815.589.456² + 116.220.651.815.589.457² + … + 116.220.651.815.589.465² + 116.220.651.815.589.466²	18
54	148.579.638.992.845.256.652.548.299.836.975.841	36
53	23.918.367.857.292.479² + 23.918.367.857.292.480² + … + 23.918.367.857.292.488² + 23.918.367.857.292.489²	17
53	6.292.971.530.524.384.774.834.250.351.792.926	34
52	20.702.293.880.386.763² + 20.702.293.880.386.764² + … + 20.702.293.880.386.772² + 20.702.293.880.386.773²	17
52	4.714.434.691.008.893.663.988.001.964.344.174	34
51	12.334.444.764.692.416² + 12.334.444.764.692.417² + … + 12.334.444.764.692.425² + 12.334.444.764.692.426²	17
51	1.673.523.804.185.731.001.375.814.083.253.761	34
50	10.606.737.485.758.644² + 10.606.737.485.758.645² + … + 10.606.737.485.758.653² + 10.606.737.485.758.654²	17
50	1.237.531.681.009.774.774.779.001.861.357.321	34
49	9.820.026.843.373.954² + 9.820.026.843.373.955² + … + 9.820.026.843.373.963² + 9.820.026.843.373.964²	16
49	1.060.762.199.250.436.336.340.529.912.670.601	34
48	2.307.176.956.796.880² + 2.307.176.956.796.881² + … + 2.307.176.956.796.889² + 2.307.176.956.796.890²	16
48	58.553.720.609.719.888.891.790.602.735.585	32
47	1.225.184.500.261.924² + 1.225.184.500.261.925² + … + 1.225.184.500.261.933² + 1.225.184.500.261.934²	16
47	16.511.847.656.502.799.720.565.674.811.561	32
46	667.440.014.425.607² + 667.440.014.425.608² + … + 667.440.014.425.616² + 667.440.014.425.617²	15
46	4.900.237.901.421.072.701.241.097.320.094	31
45	235.162.270.990.651² + 235.162.270.990.652² + … + 235.162.270.990.660² + 235.162.270.990.661²	15
45	608.314.230.672.310.013.276.032.413.806	30
44	96.737.485.169.654² + 96.737.485.169.655² + … + 96.737.485.169.663² + 96.737.485.169.664²	14
44	102.939.551.406.449.944.604.155.939.201	30
43	95.423.328.611.236² + 95.423.328.611.237² + … + 95.423.328.611.245² + 95.423.328.611.246²	14
43	100.161.728.075.737.737.570.827.161.001	30
42	29.859.187.721.278² + 29.859.187.721.279² + … + 29.859.187.721.287² + 29.859.187.721.288²	14
42	9.807.282.005.122.992.215.002.827.089	28
41	24.605.538.828.131² + 24.605.538.828.132² + … + 24.605.538.828.140² + 24.605.538.828.141²	14
41	6.659.757.951.251.991.521.597.579.566	28
40	20.445.190.077.697² + 20.445.190.077.698² + … + 20.445.190.077.706² + 20.445.190.077.707²	14
40	4.598.063.770.447.007.440.773.608.954	28
39	3.854.992.161.274² + 3.854.992.161.275² + … + 3.854.992.161.283² + 3.854.992.161.284²	13
39	163.470.610.198.747.891.016.074.361	27
38	3.138.307.807.636² + 3.138.307.807.637² + … + 3.138.307.807.645² + 3.138.307.807.646²	13
38	108.338.734.850.505.058.437.833.801	27
37	2.926.932.308.088² + 2.926.932.308.089² + … + 2.926.932.308.097² + 2.926.932.308.098²	13
37	94.236.260.097.744.779.006.263.249	26
36	2.304.066.545.900² + 2.304.066.545.901² + … + 2.304.066.545.909² + 2.304.066.545.910²	13
36	58.395.949.127.544.572.194.959.385	26
35	2.028.485.836.843² + 2.028.485.836.844² + … + 2.028.485.836.852² + 2.028.485.836.853²	13
35	45.262.302.693.222.239.620.326.254	26
34	728.081.967.850² + 728.081.967.851² + … + 728.081.967.859² + 728.081.967.860²	12
34	5.831.136.871.071.701.786.311.385	25
33	298.792.155.728² + 298.792.155.729² + … + 298.792.155.737² + 298.792.155.738²	12
33	982.044.275.603.306.572.440.289	24
32	31.113.166.954² + 31.113.166.955² + … + 31.113.166.963² + 31.113.166.964²	11
32	10.648.320.740.404.702.384.601	23
31	30.863.674.436² + 30.863.674.437² + … + 30.863.674.445² + 30.863.674.446²	11
31	10.478.230.400.000.403.287.401	23
30	30.490.910.586² + 30.490.910.587² + … + 30.490.910.595² + 30.490.910.596²	11
30	10.226.651.915.351.915.662.201	23
29	13.030.923.526² + 13.030.923.527² + … + 13.030.923.535² + 13.030.923.536²	11
29	1.867.854.648.778.464.587.681	22
28	9.757.818.186² + 9.757.818.187² + … + 9.757.818.195² + 9.757.818.196²	10
28	1.047.365.174.334.715.637.401	22
27	1.943.248.537² + 1.943.248.538² + … + 1.943.248.546² + 1.943.248.547²	10
27	41.538.363.855.836.383.514	20
26	242.363.419² + 242.363.420² + … + 242.363.428² + 242.363.429²	9
26	646.140.322.223.041.646	18
25	194.414.537² + 194.414.538² + … 194.414.546² + 194.414.547²	9
25	415.767.155.551.767.514	18
24	98.454.036² + 98.454.037² + 98.454.038² + … + 98.454.044² + 98.454.045² + 98.454.046²	8
24	106.625.180.081.526.601	18
23	35.962.406² + 35.962.407² + 35.962.408² + … + 35.962.414² + 35.962.415² + 35.962.416²	8
23	14.226.245.054.262.241	17
22	20.881.063² + 20.881.064² + 20.881.065² + … + 20.881.071² + 20.881.072² + 20.881.073²	8
22	4.796.209.009.026.974	16
21	19.357.087² + 19.357.088² + 19.357.089² + … + 19.357.095² + 19.357.096² + 19.357.097²	8
21	4.121.667.117.661.214	16
20	2.307.910² + 2.307.911² + 2.307.912² + … + 2.307.918² + 2.307.919² + 2.307.920²	7
20	58.591.188.119.585	14
19	667.883² + 667.884² + 667.885² + 667.886² + … + 667.890² + 667.891² + 667.892² + 667.893²	6
19	4.906.818.186.094	13
18	230.780² + 230.781² + 230.782² + 230.783² + … + 230.787² + 230.788² + 230.789² + 230.790²	6
18	585.878.878.585	12
17	207.677² + 207.678² + 207.679² + 207.680² + … + 207.684² + 207.685² + 207.686² + 207.687²	6
17	474.449.944.474	12
16	62.573² + 62.574² + 62.575² + 62.576² + … + 62.580² + 62.581² + 62.582² + 62.583²	5
16	43.076.067.034	11
15	24.659² + 24.660² + 24.661² + 24.662² + … + 24.666² + 24.667² + 24.668² + 24.669²	5
15	6.691.441.966	10
14	23.861² + 23.862² + 23.863² + 23.864² + … + 23.868² + 23.869² + 23.870² + 23.871²	5
14	6.265.445.626	10
13	21.107² + 21.108² + 21.109² + 21.110² + … + 21.114² + 21.115² + 21.116² + 21.117²	5
13	4.902.882.094	10
12	20.297² + 20.297² + 20.298² + 20.299² + … + 20.304² + 20.305² + 20.306² + 20.307²	5
12	4.533.883.354	10
11	2.419² + 2.420² + 2.421² + 2.422² + … + 2.426² + 2.427² + 2.428² + 2.429²	4
11	64.633.646	8
10	2.107² + 2.108² + 2.109² + 2.110² + … + 2.114² + 2.115² + 2.116² + 2.117²	4
10	49.066.094	8
9	1.216² + 1.217² + 1.218² + 1.219² + … + 1.223² + 1.224² + 1.225² + 1.226²	4
9	16.399.361	8
8	623² + 624² + 625² + 626² + 627² + 628² + 629² + 630² + 631² + 632² + 633²	3
8	4.338.334	7
7	288² + 289² + 290² + 291² + 292² + 293² + 294² + 295² + 296² + 297² + 298²	3
7	944.449	6
6	207² + 208² + 209² + 210² + 211² + 212² + 213² + 214² + 215² + 216² + 217²	3
6	494.494	6
5	126² + 127² + 128² + 129² + 130² + 131² + 132² + 133² + 134² + 135² + 126²	3
5	188.881	6
4	116² + 117² + 118² + 119² + 120² + 121² + 122² + 123² + 124² + 125² + 126²	3
4	161.161	6
3	19² + 20² + 21² + 22² + 23² + 24² + 25² + 26² + 27² + 28² + 29²	2
3	6.446	4
2	6² + 7² + 8² + 9² + 10² + 11² + 12² + 13² + 14² + 15² + 16²	1 - 2
2	1.441	4
1	4² + 5² + 6² + 7² + 8² + 9² + 10² + 11² + 12² + 13² + 14²	1 - 2
1	1.001	4

Contributions

Jean Claude Rosa - go to entry sum of 2 squares - go to entry sum of 3 squares

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Patrick De Geest - Belgium

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E-mail address : pdg@worldofnumbers.com