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Search: id:A158482
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| 15, 57, 127, 225, 351, 505, 687, 897, 1135, 1401, 1695, 2017, 2367, 2745, 3151, 3585, 4047, 4537, 5055, 5601, 6175, 6777, 7407, 8065, 8751, 9465, 10207, 10977, 11775, 12601, 13455, 14337, 15247, 16185, 17151, 18145, 19167, 20217, 21295, 22401
(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=[A158481] 49*n.^2+7 (n>0, 56, 203, 448,.,); Y=[A005843] 2*n (n>0, 2, 4, 6,.,); X = [A158482] 14*n^2+1 (n>0, 15, 57, 127, .,), we have, for all terms, Pell's equation X^2-A*Y^2=1. Example: 15^2-56*2^2=1; 57^2-203*4^2=1; 127^2-448*6^2=1.
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LINKS
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Edward Everett Withford, Pell Equation
Wolfram MathWorld, Pell Equation
Vincenzo Librandi, X^2-AY^2=1
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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)=15; n=2, a(2)=57; n=3, a(3)=127
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CROSSREFS
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Cf. A005843, A158481
Sequence in context: A043944 A140379 A020222 this_sequence A084815 A012691 A020187
Adjacent sequences: A158479 A158480 A158481 this_sequence A158483 A158484 A158485
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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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