%I A100251
%S A100251 6,2,99,35,9,15,3,0,14,8,6,21,55,4,133,10,22,0,51,27,261,15,5,85,161,9,
%T A100251 35,451,21,33,69,14,124,6,44,715,28,24,7421,217,34,16,23001,54,1065,36,
%U A100251 7,76,156,0,245
%N A100251 Let j be the smallest integer for which 1+(1+1*n)+(1+2*n)+...+(1+j*n)=k^2=s. 
               Then a(n)=k; if no such j exists, then a(n)=0.
%C A100251 Basis for sequence is shortest arithmetic series with initial term 1 
               and difference n that sums to a perfect square.
%F A100251 1+(1+1*n)+(1+2*n)+...+(1+A100254(n)*n)= 1+(1+1*n)+(1+2*n)+...+A100253(n)=a(n)^2=A100252(n)
%e A100251 a(3)=99 since 1 + 4 + 7 +...+ (1+80*3)= 99^2 = 9801 and no other arithmetic 
               series with initial term 1, difference 3 and fewer terms sums to 
               a perfect square.
%Y A100251 Sequence in context: A084249 A096039 A038256 this_sequence A020339 A154738 
               A100125
%Y A100251 Adjacent sequences: A100248 A100249 A100250 this_sequence A100252 A100253 
               A100254
%K A100251 nonn
%O A100251 1,1
%A A100251 Charlie Marion (charliemath(AT)optonline.net), Nov 21 2004