Search: id:A157362
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%I A157362
%S A157362 47,192,435,776,1215,1752,2387,3120,3951,4880,5907,7032,8255,9576,10995,
%T A157362 12512,14127,15840,17651,19560,21567,23672,25875,28176,30575,33072,
%U A157362 35667,38360,41151,44040,47027,50112,53295,56576,59955,63432,67007
%N A157362 a(n)=49*n^2-2*n (n>0)
%C A157362 If A=[A157362] 49*n.^2-2*n (47,192,435,776,...,); Y=[A157363] 686*n-14 
               (672, 1358, 2044, 2730,...,); X=[A157364] 4802*n^2-196*n+1 (4607,
               18817,42631,76049,...,) ; , we have for all terms, Pell's equation 
               X^2-A*Y^2=1. Example: 4607^2-47*672^2=1; 18817^2-192*1358^2=1; 42631^2-435*2044^2=1; 
               76049^2-776*2730^2=1.
%C A157362 If A=[A157362] 49*n.^2-2*n (n>0, 47, 192, 435,.,. ,.,); Y=[A010727] 7 
               (7,7,7,.,.,); X=[A044567] 49*n-1 (n>0, 48, 97, 146, ,. .,), we have, 
               for all terms, Pell's equation X^2-A*Y^2=1. Example: 48^2-47*7^2=1; 
               97^2-192*7^2=1; 146^2-435*7^2=1. [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), 
               Mar 12 2009]
%H A157362 Vincenzo Librandi, <a href="http://mathforum.org/kb/message.jspa?messageID=5773864&tstart=0">
               X^2-AY^2=1</a>
%H A157362 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> [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), 
               Mar 12 2009]
%H A157362 Wolfram MathWorld, <a href="http://mathworld.wolfram.com/PellEquation.html">
               Pell Equation</a> [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), 
               Mar 12 2009]
%F A157362 a(n)=49*n^2-2*n (n>0)
%e A157362 For n=1, a(1)=47, n=2, a(2)=192; n=3, a(3)=435
%Y A157362 Cf. A157363, A157364
%Y A157362 Cf. A010727, A044567 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), 
               Mar 12 2009]
%Y A157362 Sequence in context: A158632 A142413 A065532 this_sequence A141874 A142203 
               A067986
%Y A157362 Adjacent sequences: A157359 A157360 A157361 this_sequence A157363 A157364 
               A157365
%K A157362 nonn
%O A157362 1,1
%A A157362 Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Feb 28 2009

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