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Search: id:A157661
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| A157661 |
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a(n)=80000*n^2-800*n+1 (n>0) |
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+0
3
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| 79201, 318401, 717601, 1276801, 1996001, 2875201, 3914401, 5113601, 6472801, 7992001, 9671201, 11510401, 13509601, 15668801, 17988001, 20467201, 23106401, 25905601, 28864801, 31984001, 35263201, 38702401, 42301601, 46060801
(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=[A157659] 100*n.^2-n (99, 398, 897, 1596 ,..,); Y=[A157660] 8000*n-40 (7960, 15960, 23960..,); X=[A157661] 80000*n^2-800*n+1 (79201, 318401, 717601,.,), we have, for all terms, Pell's equation X^2-A*Y^2=1. Example: 79201^2-99*7960^2=1; 318401^2-398*15960^2=1; 717601^2-897*23960^2=1.
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LINKS
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Philippe Chevanne, Pell Equation
Vincenzo Librandi, X^2-AY^2=1
Wolfram MathWorld, Pell Equation
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FORMULA
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a(n)=80000*n^2-800*n+1 (n>0)
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EXAMPLE
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For n=1, a(1)=79201; n=2, a(2)=318401; n=3, a(3)=717601
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CROSSREFS
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Cf. A157659, A157660
Sequence in context: A038815 A076336 A123159 this_sequence A159713 A103873 A146324
Adjacent sequences: A157658 A157659 A157660 this_sequence A157662 A157663 A157664
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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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