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Search: id:A157666
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| A157666 |
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a(n)=19683*n-13716 (n>0) |
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+0
3
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| 5967, 25650, 45333, 65016, 84699, 104382, 124065, 143748, 163431, 183114, 202797, 222480, 242163, 261846, 281529, 301212, 320895, 340578, 360261, 379944, 399627, 419310, 438993, 458676, 478359, 498042, 517725, 537408, 557091, 576774, 596457
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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If A=[A157665] 729*n.^2-1016*n+354 (67, 1238, 3867, ,..,); Y=[A157666] 19683*n-13716 (5967, 25650, 45333,..,); X=[A157667] 531441*n^2-740664*n+258065 (48842, 902501, 2819042,..,), we have, for all terms, Pell's equation X^2-A*Y^2=1. Example: 48842^2-67*5967^2=1; 902501^2-1238*25650^2=1; 2819042^2-3867*45333^2=1.
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LINKS
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Vincenzo Librandi, X^2-AY^2=1
Wolfram MathWorld, Pell Equation
Philippe Chevanne, Pell Equation
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FORMULA
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a(n)=19683*n-13716 (n>0)
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EXAMPLE
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For n=1, a(1)=5967; n=2, a(2)=25650; n=3, a(3)=45333
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CROSSREFS
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Cf. A157665, A157667
Sequence in context: A133598 A028517 A032658 this_sequence A028546 A055108 A046903
Adjacent sequences: A157663 A157664 A157665 this_sequence A157667 A157668 A157669
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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.t), Mar 04 2009
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