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Search: id:A156627
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| 2574, 6968, 11362, 15756, 20150, 24544, 28938, 33332, 37726, 42120, 46514, 50908, 55302, 59696, 64090, 68484, 72878, 77272, 81666, 86060, 90454, 94848, 99242, 103636, 108030, 112424, 116818, 121212, 125606, 130000, 134394, 138788, 143182
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OFFSET
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1,1
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COMMENT
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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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MAPLE
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For n=1, a(1)=2574; n=2, a(2)=6968; n=3, a(3)=11362
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CROSSREFS
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Cf. A156636
Cf. A156640, A156639, A156718, A156721, A156735 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Feb 20 2009]
Sequence in context: A050544 A125492 A068265 this_sequence A031789 A001294 A109026
Adjacent sequences: A156624 A156625 A156626 this_sequence A156628 A156629 A156630
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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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