A174069 - OEIS

A174069

Numbers that can be written as a sum of at least 2 squares of consecutive positive integers.

5, 13, 14, 25, 29, 30, 41, 50, 54, 55, 61, 77, 85, 86, 90, 91, 110, 113, 126, 135, 139, 140, 145, 149, 174, 181, 190, 194, 199, 203, 204, 221, 230, 245, 255, 265, 271, 280, 284, 285, 294, 302, 313, 330, 355, 365, 366, 371, 380, 384, 385, 415, 421, 434, 446, 451

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OFFSET

1,1

COMMENTS

Numbers are listed without multiplicity: 365 is the first term that is the sum of two or more squares in more than one way. See A062681 for other numbers of that form. - M. F. Hasler, Dec 22 2013

A subsequence of A212016. This sequence focuses on the squares of consecutive positive integers. - Altug Alkan, Dec 24 2015

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

EXAMPLE

5 = 1^2 + 2^2

13 = 2^2 + 3^2

14 = 1^2 + 2^2 + 3^2

25 = 3^2 + 4^2

MATHEMATICA

max = 50^2; lst = {}; Do[z = n^2; Do[z += (n + x)^2; If[z > max, Break[]]; AppendTo[lst, z], {x, max/2}], {n, max/2}]; Union[lst]

PROG

(PARI) N=20; a=[]; for(i=2, N, for(k=1, i-1, if(N^2*2>t=sum(j=i-k, i, j^2), a=setunion(a, Set(t)), break))); a \\ M. F. Hasler, Dec 22 2013

CROSSREFS

Cf. A111774, A138591, A151557 (subset of squares), A163251 (subset of primes).