Search: id:A158403
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%I A158403
%S A158403 843,3368,7575,13464,21035,30288,41223,53840,68139,84120,101783,121128,
%T A158403 142155,164864,189255,215328,243083,272520,303639,336440,370923,407088,
%U A158403 444935,484464,525675,568568,613143,659400,707339,756960,808263,861248
%N A158403 a(n)=841*n^2+2*n (n>0)
%C A158403 If A=[A158403] 841*n.^2+2*n (n>0, 843, 3368, 7575,.,); Y=[A010868] 29 
               (29, 29, 29, ,.,); X=[A158404] 841*n+1 (n>0, 842, 1683, 2524, .,), 
               we have, for all terms, Pell's equation X^2-A*Y^2=1. Example: 842^2-843*29^2=1; 
               1683^2-3368*29^2=1; 2524^2-7575*29^2=1.
%H A158403 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 A158403 Vincenzo Librandi, <a href="http://mathforum.org/kb/message.jspa?messageID=5785989&tstart=0">
               X^2-AY^2=1</a>
%H A158403 Wolfram MathWorld, <a href="http://mathworld.wolfram.com/PellEquation.html">
               Pell Equation</a>
%F A158403 a(n)=841*n^2+2*n (n>0)
%e A158403 For n=1, a(1)=843; n=2, a(2)=3368; n=3, a(3)=7575
%Y A158403 Cf. A010868, A158404
%Y A158403 Sequence in context: A004949 A004969 A031707 this_sequence A114359 A038013 
               A078144
%Y A158403 Adjacent sequences: A158400 A158401 A158402 this_sequence A158404 A158405 
               A158406
%K A158403 nonn
%O A158403 1,1
%A A158403 Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Mar 18 2009

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