This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A100254 #5 Jul 30 2015 01:20:18
%S A100254 7,1,80,24,5,8,1,0,6,3,2,8,21,1,48,3,7,0,16,8,80,4,1,24,45,2,9,120,5,
%T A100254 8,17,3,30,1,10,168,6,5,1680,48,7,3,4960,11,224,7,1,15,31,0,48,24,16,
%U A100254 12,288,8,48,6,26,80,117,1,136160,195,13,3,9,840,1520,24,49,8,70,2,1680
%N A100254 Let j be the smallest integer for which 1 + (1+1*n) + (1+2*n) + ... + (1+j*n) = k^2 = s. Then a(n)=j; if no such j exists, then a(n)=0.
%C A100254 Basis for sequence is shortest arithmetic series with initial term 1 and difference n that sums to a perfect square.
%F A100254 1 + (1+1*n) + (1+2*n) + ... + (1+a(n)*n) = 1 + (1+1*n) + (1+2*n) + ... + A100253(n) = A100251(n)^2 = A100252(n).
%e A100254 a(3)=80 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.
%t A100254 a[n_] := Block[{k = 1}, While[ !IntegerQ[ Sqrt[(k + 1)(1 + k*n/2)]], k++ ]; k]; a[18] = a[50] = 0; Table[ a[n], {n, 75}] (* _Robert G. Wilson v_, Nov 27 2004 *)
%K A100254 nonn
%O A100254 1,1
%A A100254 _Charlie Marion_, Nov 21 2004
%E A100254 More terms from _Robert G. Wilson v_, Nov 27 2004