Search: id:A031689
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%I A031689
%S A031689 123,488,1095,1944,3035,4368,5943,7760,9819,12120,14663,16152,17448,
%T A031689 19344,20475,23744,27255,31008,35003,37284,39240,43719,48440,53403,53866,
%U A031689 58608,59093,64055,64562,67128,69744,75675,81848,88263,94920,101819
%N A031689 Least term in period of continued fraction for sqrt(n) is 11.
%C A031689 If A=[A031689] 121*n.^2+2*n (n>0) (123,488,1095,..,); Y=[A157613] 2662*n+22 
               (2684, 5346, 8008..,); X=[A157614] 29282*n^2+484*n+1 (29767, 118097, 
               264991,.,), we have, for all terms, Pell's equation X^2-A*Y^2=1. 
               Example: 29767^2-123*2684^2=1; 118097^2-488*5346^2=1; 264991^2-1095*8008^2=1. 
               [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Mar 03 2009]
%C A031689 If A=[A031689] 121*n.^2+2*n (n>0, 123, 488, 1095,.,. ,.,); Y=[A010850] 
               11 (11, 11, 11,.,); X=[A158131] 121*n+1 (n>0, 122, 243, 364, ,. .,
               ), we have, for all terms, Pell's equation X^2-A*Y^2=1. Example: 
               122^2-123*11^2=1; 243^2-488*11^2=1; 364^2-1095*11^2=1. [From Vincenzo 
               Librandi (vincenzo.librandi(AT)tin.it), Mar 13 2009]
%H A031689 Wolfram MathWorld, <a href="http://mathworld.wolfram.com/PellEquation.html">
               Pell Equation</a> [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), 
               Mar 03 2009]
%H A031689 Vincenzo Librandi, <a href="http://mathforum.org/kb/message.jspa?messageID=5771301&tstart=0">
               X^2-AY^2=1</a> [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), 
               Mar 03 2009]
%F A031689 a(n)=121*n^2+2*n (n>0) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), 
               Mar 03 2009]
%F A031689 a(n)=121*n^2+2*n (n>0) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), 
               Mar 13 2009]
%e A031689 For n=1, a(1)=123; n=2, a(2)=488; n=3, a(3)=1095 [From Vincenzo Librandi 
               (vincenzo.librandi(AT)tin.it), Mar 13 2009]
%Y A031689 Cf. A157613, A157614 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), 
               Mar 03 2009]
%Y A031689 Cf. A010850. A158131 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), 
               Mar 13 2009]
%Y A031689 Sequence in context: A004945 A004965 A091331 this_sequence A074303 A077379 
               A135475
%Y A031689 Adjacent sequences: A031686 A031687 A031688 this_sequence A031690 A031691 
               A031692
%K A031689 nonn
%O A031689 1,1
%A A031689 David W. Wilson (davidwwilson(AT)comcast.net)

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