Search: id:A100252
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%I A100252
%S A100252 36,4,9801,1225,81,225,9,0,196,64,36,441,3025,16,17689,100,484,0,2601,
%T A100252 729,68121,225,25,7225,25921,81,1225,203401,441,1089,4761,196,15376,36,
%U A100252 1936,511225,784,576,55071241,47089,1156,256,529046001,2916,1134225
%N A100252 Let j be the smallest integer for which 1+(1+1*n)+(1+2*n)+...+(1+j*n)=k^2=s. 
               Then a(n)=s; if no such j exists, then a(n)=0.
%C A100252 Basis for sequence is shortest arithmetic series with initial term 1 
               and difference n that sums to a perfect square.
%F A100252 1+(1+1*n)+(1+2*n)+...+(1+A100254(n)*n)= 1+(1+1*n)+(1+2*n)+...+A100253(n)=A100251(n)^2=a(n)
%e A100252 a(3)=9801 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 A100252 Sequence in context: A156645 A037935 A159824 this_sequence A020340 A097488 
               A109256
%Y A100252 Adjacent sequences: A100249 A100250 A100251 this_sequence A100253 A100254 
               A100255
%K A100252 nonn
%O A100252 1,1
%A A100252 Charlie Marion (charliemath(AT)optonline.net), Nov 21 2004

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