Search: id:A158444
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%I A158444
%S A158444 20,68,148,260,404,580,788,1028,1300,1604,1940,2308,2708,3140,3604,4100,
%T A158444 4628,5188,5780,6404,7060,7748,8468,9220,10004,10820,11668,12548,13460,
%U A158444 14404,15380,16388,17428,18500,19604,20740,21908,23108,24340,25604
%N A158444 a(n)=16*n^2+4 (n>0)
%C A158444 If A=[A158444] 16*n.^2+4 (n>0, 20, 68,148,.,); Y=[A005843] 2*n (n>0, 
               2, 4, 6,.,); X = [A081585] 8*n^2+1 (n>0, 9, 33, 73, .,), we have, 
               for all terms, Pell's equation X^2-A*Y^2=1. Example: 9^2-20*2^2=1; 
               33^2-68*4^2=1; 73^2-148*6^2=1.
%H A158444 Vincenzo Librandi, <a href="http://mathforum.org/kb/message.jspa?messageID=5785989&tstart=0">
               X^2-AY^2=1</a>
%H A158444 Wolfram MathWorld, <a href="http://mathworld.wolfram.com/PellEquation.html">
               Pell Equation</a>
%H A158444 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 A158444 a(n)=16*n^2+4 (n>0)
%e A158444 For n=1, a(1)=20; n=2, a(2)=68; n=3, a(3)=148
%Y A158444 Cf, A005843, A081585
%Y A158444 Sequence in context: A117432 A033577 A074632 this_sequence A145191 A044158 
               A044539
%Y A158444 Adjacent sequences: A158441 A158442 A158443 this_sequence A158445 A158446 
               A158447
%K A158444 nonn
%O A158444 1,1
%A A158444 Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Mar 19 2009

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