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Search: id:A158485
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| 13, 55, 125, 223, 349, 503, 685, 895, 1133, 1399, 1693, 2015, 2365, 2743, 3149, 3583, 4045, 4535, 5053, 5599, 6173, 6775, 7405, 8063, 8749, 9463, 10205, 10975, 11773, 12599, 13453, 14335, 15245, 16183, 17149, 18143, 19165, 20215, 21293, 22399
(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=[A158484] 49*n.^2-7 (n>0, 42, 189, 434,.,); Y=[A005843] 2*n (n>0, 2, 4, 6,.,); X = [A158485] 14*n^2-1 (n>0, 13, 55, 125, .,), we have, for all terms, Pell's equation X^2-A*Y^2=1. Example: 13^2-42*2^2=1; 55^2-189*4^2=1; 125^2-434*6^2=1.
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LINKS
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Wolfram MathWorld, Pell Equation
Vincenzo Librandi, X^2-AY^2=1
Edward Everett Withford, Pell Equation
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FORMULA
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a(n)=14*n^2-1 (n>0)
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EXAMPLE
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For n=1, a(1)=13; n=2, a(2)=55; n=3, a(3)=125
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CROSSREFS
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Cf. A005843, A158485
Sequence in context: A071230 A027000 A029531 this_sequence A005902 A051798 A061161
Adjacent sequences: A158482 A158483 A158484 this_sequence A158486 A158487 A158488
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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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