Search: id:A157324
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%I A157324
%S A157324 37,146,327,580,905,1302,1771,2312,2925,3610,4367,5196,6097,7070,8115,
%T A157324 9232,10421,11682,13015,14420,15897,17446,19067,20760,22525,24362,26271,
%U A157324 28252,30305,32430,34627,36896,39237,41650,44135,46692,49321,52022
%N A157324 a(n)=36*n^2+n (n>0)
%C A157324 If A=[A157324] 36*n^2+n (37,146,327,...,); Y=[A157325] 1728*n+24 (1752,
               3480,5208,...,); X=[A157326] 10368*n^2+288*n+1 (10657,42049,94177,
               ...,) ; , we have for all terms, Pell's equation X^2-A*Y^2=1. Example: 
               10657^2-37*1752^2=1; 42049^2-146*3480^2=1; 94177^2-327*5208^2=1; 
               167041^2-580*6936^2=1.
%H A157324 Vincenzo Librandi, <a href="http://mathforum.org/kb/message.jspa?messageID=5785989&tstart=0">
               X^2-AY^2=1</a>
%F A157324 a(n)=36*n^2+n (n>0)
%e A157324 For n=1, a(1)=37; n=2, a(2)=146; n=3, a(3)=327
%Y A157324 Cf. A157325, A157326
%Y A157324 Sequence in context: A142498 A158591 A031690 this_sequence A141968 A142656 
               A145898
%Y A157324 Adjacent sequences: A157321 A157322 A157323 this_sequence A157325 A157326 
               A157327
%K A157324 nonn
%O A157324 1,1
%A A157324 Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Feb 27 2009

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