Search: id:A156735
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%I A156735
%S A156735 9801,114243,332929,665859,1113033,1674451,2350113,3140019,4044169,
%T A156735 5062563,6195201,7442083,8803209,10278579,11868193,13572051,15390153,
%U A156735 17322499,19369089,21529923,23805001,26194323,28697889,31315699
%N A156735 a(n)=57122*n^2+47320*n+9801
%C A156735 Arises in solving Pell equations of the form X^2 - A*Y^2 = 1.
%C A156735 Let n=[A156718] (70,99,239,268,408,437,...,). If A=[A156640] (29,338,
               985,...,) or A=[156639] (29,58,425) =(n^2+1)/13^2 , Y=26*n, [A156636] 
               (1820,6214,10608,...,) or Y=[A156627] (2574,6968,11362,...,) and 
               X=2*n^2+1 [A156721] (9801,19603,143649,...,) or X=[A156735] (9801,
               114243,332929,...,) , we have for all terms, Pell's equation X^2-A*Y^2=1. 
               Example: For n=70, A=29, Y=1820, X=9801; 9801^2-29*1820^2=1; n=99, 
               A=58, Y=2574, X=19603; 19603^2-58*2574^2=1; n=239, A=338, Y=6214, 
               X=114243; 114243^2-338*6214^2=1; n=268, A=425, Y=6968, X=143649; 
               143649^2-425*6968^2=1. [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), 
               Feb 20 2009]
%H A156735 Vincenzo Librandi, <a href="http://mathforum.org/kb/message.jspa?messageID=5773147&tstart=0">
               X^2-AY^2=1</a> [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), 
               Feb 20 2009]
%e A156735 For n=0, a(0)=9801; n=1, a(1)=114243; n=2, a(2)=332929
%Y A156735 Cf. A156721
%Y A156735 Cf. A156718, A156639, A156640, A156636, A156627 [From Vincenzo Librandi 
               (vincenzo.librandi(AT)tin.it), Feb 20 2009]
%Y A156735 Sequence in context: A035911 A069333 A156721 this_sequence A113937 A036353 
               A031687
%Y A156735 Adjacent sequences: A156732 A156733 A156734 this_sequence A156736 A156737 
               A156738
%K A156735 nonn
%O A156735 1,1
%A A156735 Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Feb 15 2009

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