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A174069
Numbers that can be written as a sum of at least 2 squares of consecutive positive integers.
12
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
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
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).
See also A062681, A212016.
Sequence in context: A191382 A291792 A292565 * A020996 A090759 A090758
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
Name edited by Altug Alkan, Dec 24 2015
STATUS
approved