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%I #14 Jan 01 2018 11:51:55
%S 1,4,2,0,3,11,4,1,5,18,6,0,7,25,8,0,9,4,10,0,11,39,12,2,4,46,14,0,15,
%T 53,16,9,17,60,18,0,19,67,20,3,21,74,22,0,23,81,24,0,1,16,26,0,27,11,
%U 28,4,29,102,30,0,31,109,32,0,33,116,34,0,35,123,36,5,37,130,11,0,39
%N a(n) = start of the smallest string of n consecutive positive integers with a square sum, or 0 if no such number exists.
%C Equivalently, smallest k such that n(n+2k-1)/2 is a square, 0 if there is no such square. - _Ralf Stephan_, Mar 23 2003
%C a(n)=0 if and only if n has the form 4^e*m with e > 0 and m odd. - _Dean Hickerson_, Mar 25 2003
%C a(k) = 1 if k is the index of a square triangular number, i.e., k(k+1)/2 is a square, or if k belongs to A001108. If n is odd then a(n) <= (n+1)/2.
%H Clement Martin, <a href="/A076114/b076114.txt">Table of n, a(n) for n = 1..10000</a>
%e a(2) = 4, 4+5 = 9 = 3^2. a(8) = 1, 1+2+3+4+5+6+7+8 = 36 = 6^2.
%o (PARI) for(n=1,100,o=n*(n+1)/2:k=0:while(k<10^5&&!issquare(o+n*k),k=k+1): if(k>=10^5,k=-1):print1(k+1","))
%Y Cf. A001108, A001109, A076115.
%K nonn
%O 1,2
%A _Amarnath Murthy_, Oct 09 2002
%E More terms from _Ralf Stephan_, Mar 23 2003
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