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 A097812 Numbers n such that n^2 is the sum of two or more consecutive positive squares. 8
 5, 29, 70, 77, 92, 106, 138, 143, 158, 169, 182, 195, 245, 253, 274, 357, 385, 413, 430, 440, 495, 531, 650, 652, 655, 679, 724, 788, 795, 985, 1012, 1022, 1055, 1133, 1281, 1365, 1397, 1518, 1525, 1529, 1546, 1599, 1612, 1786, 1828, 2205, 2222, 2257, 2372 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS These numbers were found by exhaustive search. The sums are not unique; for n = 143, there are two representations. The Mathematica code prints n, the range of squares in the sum and the number of squares in the sum. Because the search included sums of all squares up to 2000, this sequence is complete up to 2828. LINKS Donovan Johnson, Table of n, a(n) for n = 1..5077 K. S. Brown, Sum of Consecutive Nth Powers Equals an Nth Power EXAMPLE 29 is in this sequence because 20^2 + 21^2 = 29^2. Contribution from Donovan Johnson, Feb 19 2011: (Start) For seven terms < (10^15)^(1/2), the square is a sum in two different ways: 143^2 = 7^2 + ... + 39^2 = 38^2 + ... + 48^2. 2849^2 = 294^2 + ... + 367^2 = 854^2 + ... + 864^2. 208395^2 = 2175^2 + ... + 5199^2 = 29447^2 + ... + 29496^2. 2259257^2 = 9401^2 + ... + 25273^2 = 26181^2 + ... + 32158^2. 6555549^2 = 41794^2 + ... + 58667^2 = 87466^2 + ... + 92756^2. 11818136^2 = 10898^2 + ... + 74906^2 = 29929^2 + ... + 76392^2. 19751043^2 = 39301^2 + ... + 107173^2 = 249217^2 + ... + 255345^2. (End) MATHEMATICA g[m0_, m1_] := (1 - m0 + m1)(-m0 + 2m0^2 + m1 + 2m0 m1 + 2m1^2)/6; A097812 = {}; Do[n = g[m0, m1]^(1/2); If[IntegerQ[n], Print[{n, m0, m1, m1 - m0 + 1}]; AppendTo[A097812, n]], {m1, 2, 2000}, {m0, m1 - 1, 1, -1}]; Union[A097812] CROSSREFS Cf. A097811 (n^3 is the sum of consecutive cubes). Cf. A001032, A151557. Sequence in context: A301858 A293174 A108928 * A176333 A100559 A224498 Adjacent sequences:  A097809 A097810 A097811 * A097813 A097814 A097815 KEYWORD nonn AUTHOR T. D. Noe, Aug 25 2004 EXTENSIONS Name edited by Altug Alkan, Dec 07 2015 STATUS approved

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Last modified October 14 17:43 EDT 2019. Contains 328022 sequences. (Running on oeis4.)