Search: id:A157507
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%I A157507
%S A157507 79,320,723,1288,2015,2904,3955,5168,6543,8080,9779,11640,13663,15848,
%T A157507 18195,20704,23375,26208,29203,32360,35679,39160,42803,46608,50575,
%U A157507 54704,58995,63448,68063,72840,77779,82880,88143,93568,99155,104904
%N A157507 a(n)=81*n^2-2*n (n>0)
%C A157507 If A=[A157507] 81*n.^2-2*n (79,320,723,1288,.,); Y=[A157508] 1458*n-18 
               (1440,2898,4356..,); X=[A157509] 13122*n^2-324*n+1 (12799,51841,117127,
               .,) ; , we have for all terms, Pell's equation X^2-A*Y^2=1. Example: 
               12799^2-79*1440^2=1; 51841^2-320*2898^2=1; 117127^2-723*4356^2=1.
%C A157507 If A=[A157507] 81*n.^2-2*n (n>0, 79, 320, 723,.,. ,.,); Y=[A010734] 9 
               (9,9,9,.,..,); X=[A044712] 81*n-1 (n>0, 80, 161, 242, ,. .,), we 
               have, for all terms, Pell's equation X^2-A*Y^2=1. Example: 80^2-79*9^2=1; 
               161^2-320*9^2=1; 242^2-723*9^2=1. [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), 
               Mar 13 2009]
%H A157507 Vincenzo Librandi, <a href="http://mathforum.org/kb/message.jspa?messageID=5771301&tstart=0">
               X^2-AY^2=1</a>
%H A157507 Wolfram MathWorld, <a href="http://mathworld.wolfram.com/PellEquation.html">
               Pell Equation</a>
%F A157507 a(n)=81*n^2-2*n (n>0)
%e A157507 For n=1, a(1)=79; n=2, a(2)=320; n=3, a(3)=723
%Y A157507 Cf. A157508, A157509
%Y A157507 Cf. A010734, A044712 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), 
               Mar 13 2009]
%Y A157507 Sequence in context: A082077 A158769 A158774 this_sequence A142897 A142330 
               A007254
%Y A157507 Adjacent sequences: A157504 A157505 A157506 this_sequence A157508 A157509 
               A157510
%K A157507 nonn
%O A157507 1,1
%A A157507 Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Mar 02 2009

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