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Search: id:A156640
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| 29, 338, 985, 1970, 3293, 4954, 6953, 9290, 11965, 14978, 18329, 22018, 26045, 30410, 35113, 40154, 45533, 51250, 57305, 63698, 70429, 77498, 84905, 92650, 100733, 109154, 117913, 127010, 136445, 146218, 156329, 166778
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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)=338; n=2, a(2)=985; n=3, a(3)=1970
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CROSSREFS
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Cf. A156639
Cf. A156718, A!56636, A156627, A156721, A156735 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Feb 20 2009]
Sequence in context: A057131 A160442 A125417 this_sequence A022689 A077516 A142278
Adjacent sequences: A156637 A156638 A156639 this_sequence A156641 A156642 A156643
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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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