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Search: id:A157910
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| 17, 71, 161, 287, 449, 647, 881, 1151, 1457, 1799, 2177, 2591, 3041, 3527, 4049, 4607, 5201, 5831, 6497, 7199, 7937, 8711, 9521, 10367, 11249, 12167, 13121, 14111, 15137, 16199, 17297, 18431, 19601, 20807, 22049, 23327, 24641, 25991, 27377, 28799
(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=[A157909] 81*n.^2-9 (72,315,720,.,); Y=[A005843] 2*n (n>0, 2,4,6,8,.,); X=[A157910] 18*n^2-1 (17, 71, 161,..,), we have, for all terms, Pell's equation X^2-A*Y^2=1. Example: 17^2-72 *2^2=1; 71^2-315*4^2=1; 161^2-720*6^2=1.
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LINKS
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Edward Everett Withford, Pell Equation
Vincenzo Librandi, X^2-AY^2=1
Wolfram MathWorld, Pell Equation
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FORMULA
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a(n)=18*n^2-1 (n>0)
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EXAMPLE
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For n=1, a(1)=17; n=2, a(2)=71; n=3, a(3)=161
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CROSSREFS
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Cf. A157909, A005843
Sequence in context: A044010 A106921 A105414 this_sequence A141959 A069496 A047978
Adjacent sequences: A157907 A157908 A157909 this_sequence A157911 A157912 A157913
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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 09 2009
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