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Search: id:A157914
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| 7, 31, 71, 127, 199, 287, 391, 511, 647, 799, 967, 1151, 1351, 1567, 1799, 2047, 2311, 2591, 2887, 3199, 3527, 3871, 4231, 4607, 4999, 5407, 5831, 6271, 6727, 7199, 7687, 8191, 8711, 9247, 9799, 10367, 10951, 11551, 12167, 12799, 13447, 14111, 14791
(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=[A157913] 64*n.^2-16 (48, 240, 560,.,); Y=[A000027] n (1, 2, 3, 4, ,.,); X=[A157914] 8*n^2 - 1 (n>0, 7, 31, 71..,), we have, for all terms, Pell's equation X^2-A*Y^2=1. Example: 7^2-48 *1\^2=1; 31^2-240*2^2=1; 71^2-560*3^2=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)=8*n^2-1 (n>0)
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EXAMPLE
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For n=1, a(1)=7; n=2, a(2)=31; n=3, a(3)=71
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CROSSREFS
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Cf. A000027, A157913
Sequence in context: A163354 A105428 A050547 this_sequence A090684 A033199 A003550
Adjacent sequences: A157911 A157912 A157913 this_sequence A157915 A157916 A157917
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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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