%I #25 May 02 2018 10:09:19

%S 1,3,5,2,9,11,13,15,3,19,6,5,25,27,29,4,33,10,37,39,14,43,45,7,5,9,53,

%T 55,57,59,61,18,65,67,15,6,18,75,22,9,81,83,15,87,21,26,12,95,7,99,

%U 101,33,30,107,109,111,22,25,117,11,121,42,125,8,129

%N Let j be the smallest integer for which n+(n+1)+...+(n+j) is a square, say k^2; then a(n)=k.

%C Basis for sequence is shortest arithmetic sequence with initial term n and difference 1 that sums to a perfect square. Cf. A100251, A100252, A100253, A100254.

%C a(n) is the least k>0 such that triangular(n-1) + k^2 is a triangular number. - _Alex Ratushnyak_, May 17 2013

%H Shawn A. Broyles, <a href="/A101157/b101157.txt">Table of n, a(n) for n = 1..1000</a>

%F n+(n+1)+...+(n+A101160(n)) = n+(n+1)+...+A101159(n) = a(n)^2 = A101158(n).

%F a(n^2) = n. - _Michel Marcus_, Jun 28 2013

%e a(11)=6 since 11+12+13 = 6^2.

%o (PARI) a(n) = {j = 0; while(! issquare(v=sum(k=0, j, n+k)), j++); sqrtint(v);} \\ _Michel Marcus_, Sep 01 2013

%Y Cf. A101158, A101159, A101160.

%K nonn

%O 1,2

%A _Charlie Marion_, Dec 29 2004

%E More terms from _Michel Marcus_, Jun 28 2013