cp's OEIS Frontend

A174069 Numbers that can be written as a sum of at least 2 squares of consecutive positive integers.

%I A174069 #32 Jan 09 2016 19:33:21
%S A174069 5,13,14,25,29,30,41,50,54,55,61,77,85,86,90,91,110,113,126,135,139,
%T A174069 140,145,149,174,181,190,194,199,203,204,221,230,245,255,265,271,280,
%U A174069 284,285,294,302,313,330,355,365,366,371,380,384,385,415,421,434,446,451
%N A174069 Numbers that can be written as a sum of at least 2 squares of consecutive positive integers.
%C A174069 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
%C A174069 A subsequence of A212016. This sequence focuses on the squares of consecutive positive integers. - _Altug Alkan_, Dec 24 2015
%H A174069 Vincenzo Librandi, <a href="/A174069/b174069.txt">Table of n, a(n) for n = 1..1000</a>
%e A174069 5 = 1^2 + 2^2
%e A174069 13 = 2^2 + 3^2
%e A174069 14 = 1^2 + 2^2 + 3^2
%e A174069 25 = 3^2 + 4^2
%t A174069 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]
%o A174069 (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
%Y A174069 Cf. A111774, A138591, A151557 (subset of squares), A163251 (subset of primes).
%Y A174069 See also A062681, A212016.
%K A174069 nonn,easy
%O A174069 1,1
%A A174069 _Vladimir Joseph Stephan Orlovsky_, Mar 06 2010
%E A174069 Name edited by _Altug Alkan_, Dec 24 2015