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Search: id:A156721
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| 9801, 19603, 143649, 381939, 734473, 1201251, 1782273, 2477539, 3287049, 4210803, 5248801, 6401043, 7667529, 9048259, 10543233, 12152451, 13875913, 15713619, 17665569, 19731763, 21912201, 24206883, 26615809, 29138979
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OFFSET
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1,1
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COMMENT
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57122*n^2-47320*n+9801
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]
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LINKS
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Vincenzo Librandi, X^2-AY^2=1 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Feb 20 2009]
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EXAMPLE
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For n=0, a(0)=9801; n=1, a(1)=19603; n=2, a(2)=143649
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CROSSREFS
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Cf. A156735
Cf. A156718, A156639, A156640, A156636, A156627 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Feb 20 2009]
Sequence in context: A145209 A035911 A069333 this_sequence A156735 A113937 A036353
Adjacent sequences: A156718 A156719 A156720 this_sequence A156722 A156723 A156724
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KEYWORD
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nonn
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AUTHOR
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Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Feb 15 2009
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