Search: id:A157857
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%I A157857
%S A157857 3599,14398,32397,57596,89995,129594,176393,230392,291591,359990,435589,
%T A157857 518388,608387,705586,809985,921584,1040383,1166382,1299581,1439980,
%U A157857 1587579,1742378,1904377,2073576,2249975,2433574,2624373,2822372
%N A157857 a(n)=3600*n^2-n (n>0)
%C A157857 If A=[A157857] 3600*n.^2-n (3599, 14398, 32397,.,); Y=[A157858] 1728000*n 
               -240 (1727760, 3455760..,); X=[A157859] 103680000*n^2-28800*n +1 
               (103651201, 414662401,.,), we have, for all terms, Pell's equation 
               X^2-A*Y^2=1. Example: 103651201^2-3599 *1727760^2=1; 414662401^2-14398*3455760^2=1.
%H A157857 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 A157857 Vincenzo Librandi, <a href="http://mathforum.org/kb/message.jspa?messageID=5785989&tstart=0">
               X^2-AY^2=1</a>
%H A157857 Wolfram MathWorld, <a href="http://mathworld.wolfram.com/PellEquation.html">
               Pell Equation</a>
%F A157857 a(n)=3600*n^2-n (n>0)
%e A157857 For n=1, a(1)=3599; n=2, a(2)=14398; n=3, a(3)=32397
%Y A157857 Cf. A157858, A157859
%Y A157857 Sequence in context: A004952 A004972 A156845 this_sequence A141781 A096472 
               A027824
%Y A157857 Adjacent sequences: A157854 A157855 A157856 this_sequence A157858 A157859 
               A157860
%K A157857 nonn
%O A157857 1,1
%A A157857 Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Mar 08 2009

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