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Search: id:A156639
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| 29, 58, 425, 1130, 2173, 3554, 5273, 7330, 9725, 12458, 15529, 18938, 22685, 26770, 31193, 35954, 41053, 46490, 52265, 58378, 64829, 71618, 78745, 86210, 94013, 102154, 110633, 119450, 128605, 138098, 147929, 158098
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OFFSET
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1,1
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COMMENT
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Arises in solving Pell equations of the form X^2 - A*Y^2 = 1.
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)=29; n=1, a(1)=58; n=2, a(2)=425
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CROSSREFS
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Cf. A156640
Cf. A156718, A156636, A156627, A156721, A156735 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Feb 20 2009]
Sequence in context: A004922 A004942 A033904 this_sequence A080170 A078848 A055784
Adjacent sequences: A156636 A156637 A156638 this_sequence A156640 A156641 A156642
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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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