Search: id:A157958
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%I A157958
%S A157958 243,485,727,969,1211,1453,1695,1937,2179,2421,2663,2905,3147,3389,3631,
%T A157958 3873,4115,4357,4599,4841,5083,5325,5567,5809,6051,6293,6535,6777,7019,
%U A157958 7261,7503,7745,7987,8229,8471,8713,8955,9197,9439,9681,9923,10165
%N A157958 a(n)=242*n+1 (n>0)
%C A157958 If A=[A031700] 121*n.^2+n (122, 486, 1092,. ,.,); Y=[A010861] 20 (20, 
               20, 20,..,); X=[A157958] 242*n+1 (243, 485, 727, ,. .,), we have, 
               for all terms, Pell's equation X^2-A*Y^2=1. Example: 243^2-122 *22^2=1; 
               485^2-486*22^2=1; 727^2-1092*22^2=1.
%H A157958 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 A157958 Vincenzo Librandi, <a href="http://mathforum.org/kb/message.jspa?messageID=5785989&tstart=0">
               X^2-AY^2=1</a>
%H A157958 Wolfram MathWorld, <a href="http://mathworld.wolfram.com/PellEquation.html">
               Pell Equation</a>
%F A157958 a(n)=242*n+1 (n>0)
%e A157958 For n=1, a(1)=243; n=2, a(2)=485; n=3, a(3)=727
%Y A157958 Cf. A031700, A010861
%Y A157958 Sequence in context: A018871 A046318 A046375 this_sequence A067838 A113335 
               A100627
%Y A157958 Adjacent sequences: A157955 A157956 A157957 this_sequence A157959 A157960 
               A157961
%K A157958 nonn
%O A157958 1,1
%A A157958 Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Mar 10 2009

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