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Search: id:A158254
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| 291, 1160, 2607, 4632, 7235, 10416, 14175, 18512, 23427, 28920, 34991, 41640, 48867, 56672, 65055, 74016, 83555, 93672, 104367, 115640, 127491, 139920, 152927, 166512, 180675, 195416, 210735, 226632, 243107, 260160, 277791, 296000, 314787
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OFFSET
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1,1
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COMMENT
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If A=[A158254] 289*n.^2+2*n (n>0, 291, 1160, 2607, ,.,); Y=[A010856] 17 (17, 17, 17 ,.,); X=[A158255] 289*n+1 (n>0, 290, 579, 868, .,), we have, for all terms, Pell's equation X^2-A*Y^2=1. Example: 290^2-291*17^2=1; 579^2-1160*17^2=1; 868^2-2607*17^2=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)=289*n^2+2*n (n>0)
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EXAMPLE
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For n=1, a(1)=291; n=2, a(2)=1160; n=3, a(3)=2607
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CROSSREFS
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Cf. A010856, A158255
Sequence in context: A090890 A123913 A031695 this_sequence A088892 A098248 A048956
Adjacent sequences: A158251 A158252 A158253 this_sequence A158255 A158256 A158257
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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 15 2009
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