Search: id:A156721
Results 1-1 of 1 results found.

%I A156721
%S A156721 9801,19603,143649,381939,734473,1201251,1782273,2477539,3287049,
%T A156721 4210803,5248801,6401043,7667529,9048259,10543233,12152451,13875913,
%U A156721 15713619,17665569,19731763,21912201,24206883,26615809,29138979
%N A156721 57122*n^2-47320*n+9801
%C A156721 57122*n^2-47320*n+9801
%C A156721 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 A156721 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 A156721 For n=0, a(0)=9801; n=1, a(1)=19603; n=2, a(2)=143649
%Y A156721 Cf. A156735
%Y A156721 Cf. A156718, A156639, A156640, A156636, A156627 [From Vincenzo Librandi 
               (vincenzo.librandi(AT)tin.it), Feb 20 2009]
%Y A156721 Sequence in context: A145209 A035911 A069333 this_sequence A156735 A113937 
               A036353
%Y A156721 Adjacent sequences: A156718 A156719 A156720 this_sequence A156722 A156723 
               A156724
%K A156721 nonn
%O A156721 1,1
%A A156721 Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Feb 15 2009

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