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%I #2 Mar 30 2012 17:23:21
%S 8,3,241,97,26,49,8,0,55,31,23,97,274,15,721,49,120,0,305,161,1681,89,
%T 24,577,1126,53,244,3361,146,241,528,97,991,35,351,6049,223,191,65521,
%U 1921,288,127,213281,485,10081,323,48,721,1520,0,2449
%N Let j be the smallest integer for which 1+(1+1*n)+(1+2*n)+...+(1+j*n)=k^2=s. Then a(n)=1+j*n; if no such j exists, then a(n)=0.
%C Basis for sequence is shortest arithmetic series with initial term 1 and difference n that sums to a perfect square.
%F 1+(1+1*n)+(1+2*n)+...+(1+A100254(n)*n)= 1+(1+1*n)+(1+2*n)+...+a(n)=A100251(n)^2=A100252(n)
%e a(3)=241 since 1 + 4 + 7 +...+ 241 = 99^2 = 9801 and no other arithmetic series with initial term 1, difference 3 and fewer terms sums to a perfect square.
%K nonn
%O 1,1
%A _Charlie Marion_, Nov 21 2004