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Search: id:A157670
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| A157670 |
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a(n)=531441*n^2-322218*n+48842 (n>0) |
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+0
3
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| 258065, 1530170, 3865157, 7263026, 11723777, 17247410, 23833925, 31483322, 40195601, 49970762, 60808805, 72709730, 85673537, 99700226, 114789797, 130942250, 148157585, 166435802, 185776901, 206180882, 227647745, 250177490
(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=[A157668] 729*n.^2-442*n+67 (354, 2099, 5302, ,..,); Y=[A157669] 19683*n-5967 (13716, 33399, 53082,..,); X=[A157670] 531441*n^2-322218*n+48842 (258065, 1530170, 3865157,..,), we have, for all terms, Pell's equation X^2-A*Y^2=1. Example: 258065^2-354*13716^2=1; 1530170^2-2099*33399^2=1; 3865157^2-5302*53082^2=1.
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LINKS
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Wolfram MathWorld, Pell Equation
Vincenzo Librandi, X^2-AY^2=1
Philippe Chevanne, Pell Equation
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FORMULA
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a(n)=531441*n^2-322218*n+48842 (n>0)
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EXAMPLE
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For n=1, a(1)=258065; n=2, a(2)=1530170; n=3, a(3)=3865157
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CROSSREFS
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Cf. A157668, A157669
Sequence in context: A105656 A105657 A065794 this_sequence A153980 A146897 A002272
Adjacent sequences: A157667 A157668 A157669 this_sequence A157671 A157672 A157673
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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), Mar 04 2009
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