Search: id:A157729
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%I A157729
%S A157729 423812499,1821906249,4196562499,7547781249,11875562499
%N A157729 a(n)=488281250*n^2-66750000*n+2281249 (n>0)
%C A157729 If A=[A157727] 15625*n.^2-2136*n+73 (13562, 58301, 134290, ,..,); Y=[A157728] 
               3906250*n- 267000 (3639250, 7545500,..,); X=[A157729] 488281250*n^2-66750000*n 
               + 2281249 (423812499, 1821906249,..,), we have, for all terms, Pell's 
               equation X^2-A*Y^2=1. Example: 423812499^2-13562*3639250^2=1; 1821906249^2-58301*7545500^2=1.
%H A157729 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 A157729 Vincenzo Librandi, <a href="http://mathforum.org/kb/message.jspa?messageID=5773864&tstart=0">
               X^2-AY^2=1</a>
%H A157729 Wolfram MathWorld, <a href="http://mathworld.wolfram.com/PellEquation.html">
               Pell Equation</a>
%F A157729 a(n)=488281250*n^2-66750000*n+2281249 (n>0)
%e A157729 For n=1, a(1)=42381249; n=2, a(2)=1821906249; n=3, a(3)=4196562499
%Y A157729 Cf. A157727, A157728
%Y A157729 Sequence in context: A038132 A101770 A166024 this_sequence A017408 A017528 
               A117631
%Y A157729 Adjacent sequences: A157726 A157727 A157728 this_sequence A157730 A157731 
               A157732
%K A157729 nonn
%O A157729 1,1
%A A157729 Vincenzo Librandi (vincenzo.librandi(AT)tinit), Mar 05 2009

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