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Search: id:A158132
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| 146, 580, 1302, 2312, 3610, 5196, 7070, 9232, 11682, 14420, 17446, 20760, 24362, 28252, 32430, 36896, 41650, 46692, 52022, 57640, 63546, 69740, 76222, 82992, 90050, 97396, 105030, 112952, 121162, 129660, 138446, 147520, 156882, 166532
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OFFSET
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1,1
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COMMENT
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If A=[A158132] 144*n.^2+2*n (n>0, 146, 580, 1302,.,. ,.,); Y=[A010851] 12 (12, 12, 12,.,); X=[A1581333] 144*n+1 (n>0, 145, 289, 433, ,. .,), we have, for all terms, Pell's equation X^2-A*Y^2=1. Example: 145^2-146*12^2=1; 289^2-580*12^2=1; 433^2-1302*12^2=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)=144*n^2+2*n (n>0)
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EXAMPLE
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For n=1, a(1)=146; n=2, a(2)=580; n=3, a(3)=1302
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CROSSREFS
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Cf, A010851, A158133
Sequence in context: A145915 A119379 A118699 this_sequence A043431 A166219 A097728
Adjacent sequences: A158129 A158130 A158131 this_sequence A158133 A158134 A158135
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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 13 2009
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