Search: id:A157872
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%I A157872
%S A157872 6,33,78,141,222,321,438,573,726,897,1086,1293,1518,1761,2022,2301,2598,
%T A157872 2913,3246,3597,3966,4353,4758,5181,5622,6081,6558,7053,7566,8097,8646,
%U A157872 9213,9798,10401,11022,11661,12318,12993,13686,14397,15126,15873,16638
%N A157872 a(n)=9*n^2-3 (n>0)
%C A157872 If A=[A157872] 9*n.^2-3 (6, 33, 78, 141,.,); Y=[A005843] 2*n (except 
               the first term , 2,4,6,8,.,); X=[A140811] 6*n^2-1 (except the first 
               term, 5,23,5395,.,), we have, for all terms, Pell's equation X^2-A*Y^2=1. 
               Example: 5^2-6 *2^2=1; 23^2-33*4^2=1; 53^2-78*6^2=1.
%H A157872 Edward Everett Withford, <a href="http://quod.lib.umich.edu/cgi/t/text/
               text-idx?c=umhistmath;cc=umhistmath;idno=abv2773.0001.001;view=toc">
               Pell Equation</a>
%H A157872 Vincenzo Librandi, <a href="http://mathforum.org/kb/message.jspa?messageID=5785989&tstart=0">
               X^2-AY^2=1</a>
%H A157872 Wolfram MathWorld, <a href="http://mathworld.wolfram.com/PellEquation.html">
               Pell Equation</a>
%F A157872 a(n)=9*n^2-3 (n>0)
%e A157872 For n=1, a(1)=3; n=2, a(2)=33; n=3, a(3)=78
%Y A157872 Cf. A005843, A140811
%Y A157872 Sequence in context: A140521 A069065 A073343 this_sequence A153127 A135526 
               A057818
%Y A157872 Adjacent sequences: A157869 A157870 A157871 this_sequence A157873 A157874 
               A157875
%K A157872 nonn
%O A157872 1,1
%A A157872 Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Mar 08 2009

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