Search: id:A158485
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%I A158485
%S A158485 13,55,125,223,349,503,685,895,1133,1399,1693,2015,2365,2743,3149,3583,
%T A158485 4045,4535,5053,5599,6173,6775,7405,8063,8749,9463,10205,10975,11773,
%U A158485 12599,13453,14335,15245,16183,17149,18143,19165,20215,21293,22399
%N A158485 a(n)=14*n^2-1 (n>0)
%C A158485 If A=[A158484] 49*n.^2-7 (n>0, 42, 189, 434,.,); Y=[A005843] 2*n (n>0, 
               2, 4, 6,.,); X = [A158485] 14*n^2-1 (n>0, 13, 55, 125, .,), we have, 
               for all terms, Pell's equation X^2-A*Y^2=1. Example: 13^2-42*2^2=1; 
               55^2-189*4^2=1; 125^2-434*6^2=1.
%H A158485 Wolfram MathWorld, <a href="http://mathworld.wolfram.com/PellEquation.html">
               Pell Equation</a>
%H A158485 Vincenzo Librandi, <a href="http://mathforum.org/kb/message.jspa?messageID=5785989&tstart=0">
               X^2-AY^2=1</a>
%H A158485 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>
%F A158485 a(n)=14*n^2-1 (n>0)
%e A158485 For n=1, a(1)=13; n=2, a(2)=55; n=3, a(3)=125
%Y A158485 Cf. A005843, A158485
%Y A158485 Sequence in context: A071230 A027000 A029531 this_sequence A005902 A051798 
               A061161
%Y A158485 Adjacent sequences: A158482 A158483 A158484 this_sequence A158486 A158487 
               A158488
%K A158485 nonn
%O A158485 1,1
%A A158485 Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Mar 20 2009

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