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

1,1

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).

See also A062681, A212016.

Sequence in context: A191382 A291792 A292565 * A020996 A090759 A090758

Adjacent sequences: A174066 A174067 A174068 * A174070 A174071 A174072

Keyword

nonn,easy

Author

Vladimir Joseph Stephan Orlovsky, Mar 06 2010

Extensions

Name edited by Altug Alkan, Dec 24 2015

Status

approved