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

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, Mar 06 2010

Keywords

• nonn
• easy

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

Examples

			5 = 1^2 + 2^2
13 = 2^2 + 3^2
14 = 1^2 + 2^2 + 3^2
25 = 3^2 + 4^2
		

Links

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

Crossrefs

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

See also A062681, A212016.

Programs

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]

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

Extensions

Name edited by Altug Alkan, Dec 24 2015