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Search: id:A158488
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| 72, 264, 584, 1032, 1608, 2312, 3144, 4104, 5192, 6408, 7752, 9224, 10824, 12552, 14408, 16392, 18504, 20744, 23112, 25608, 28232, 30984, 33864, 36872, 40008, 43272, 46664, 50184, 53832, 57608, 61512, 65544, 69704, 73992, 78408, 82952
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OFFSET
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1,1
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COMMENT
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If A=[A158488] 64*n.^2+8 (n>0, 72, 264, 584,.,); Y=[A005843] 2*n (n>0, 2, 4, 6,.,); X = [A108211] 16*n^2-1 (n>0, 17, 65, 145, .,), we have, for all terms, Pell's equation X^2-A*Y^2=1. Example: 17^2-72*2^2=1; 65^2-264*4^2=1; 145^2-584*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)=64*n^2+8 (n>0)
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EXAMPLE
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For n=1, a(1)=72; n=2, a(2)=264; n=3, a(3)=584
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CROSSREFS
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Cf. A005843, A108211
Sequence in context: A064716 A073412 A019507 this_sequence A165139 A004007 A157909
Adjacent sequences: A158485 A158486 A158487 this_sequence A158489 A158490 A158491
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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 20 2009
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