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Search: id:A157509
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| 12799, 51841, 117127, 208657, 326431, 470449, 640711, 837217, 1059967, 1308961, 1584199, 1885681, 2213407, 2567377, 2947591, 3354049, 3786751, 4245697, 4730887, 5242321, 5779999, 6343921, 6934087, 7550497, 8193151, 8862049
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OFFSET
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1,1
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COMMENT
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If A=[A157507] 81*n.^2-2*n (79,320,723,1288,.,); Y=[A157508] 1458*n-18 (1440,2898,4356..,); X=[A157509] 13122*n^2-324*n+1 (12799,51841,117127,.,) ; , we have for all terms, Pell's equation X^2-A*Y^2=1. Example: 12799^2-79*1440^2=1; 51841^2-320*2898^2=1; 117127^2-723*4356^2=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)=13122*n^2-324*n+1
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EXAMPLE
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For n=1, a(1)=12799; n=2, a(2)=51841; n=3, a(3)=117127
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CROSSREFS
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Cf. A157507, A157508
Sequence in context: A105655 A124411 A163573 this_sequence A035916 A024752 A024760
Adjacent sequences: A157506 A157507 A157508 this_sequence A157510 A157511 A157512
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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 02 2009
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