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Search: id:A157614
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| A157614 |
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a(n)=29282*n^2+484*n+1 (n>0) |
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+0
3
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| 29767, 118097, 264991, 470449, 734471, 1057057, 1438207, 1877921, 2376199, 2933041, 3548447, 4222417, 4954951, 5746049, 6595711, 7503937, 8470727, 9496081, 10579999, 11722481, 12923527, 14183137, 15501311, 16878049, 18313351
(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=[A031689] 121*n.^2+2*n (n>0) (123,488,1095,..,); Y=[A157613] 2662*n+22 (2684, 5346, 8008..,); X=[A157614] 29282*n^2+484*n+1 (29767, 118097, 264991,.,), we have, for all terms, Pell's equation X^2-A*Y^2=1. Example: 29767^2-123*2684^2=1; 118097^2-488*5346^2=1; 264991^2-1095*8008^2=1.
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LINKS
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Vincenzo Librandi, X^2-AY^2=1
Wolfram MathWorld, Pell Equation
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FORMULA
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a(n)=29282*n^2+484*n+1 (n>0)
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EXAMPLE
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For n=1, a(1)=29767; n=2, a(2)=118097; n=3, a(3)=264991
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CROSSREFS
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Cf. A031689, A157613
Sequence in context: A022200 A158933 A056747 this_sequence A106771 A074969 A066765
Adjacent sequences: A157611 A157612 A157613 this_sequence A157615 A157616 A157617
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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 03 2009
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