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Search: id:A158123
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| 82, 163, 244, 325, 406, 487, 568, 649, 730, 811, 892, 973, 1054, 1135, 1216, 1297, 1378, 1459, 1540, 1621, 1702, 1783, 1864, 1945, 2026, 2107, 2188, 2269, 2350, 2431, 2512, 2593, 2674, 2755, 2836, 2917, 2998, 3079, 3160, 3241, 3322, 3403, 3484, 3565
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OFFSET
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1,1
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COMMENT
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If A=[A031433] 81*n.^2+2*n (n>0, 83, 328, 735,.,. ,.,); Y=[A010734] 9 (9,9,9,.,..,); X=[A158123] 81*n+1 (n>0, 82, 163, 244, ,. .,), we have, for all terms, Pell's equation X^2-A*Y^2=1. Example: 82^2-83*9^2=1; 163^2-328*9^2=1; 244^2-735*9^2=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)=81*n+1 (n>0)
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EXAMPLE
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For n=1, a(1)=82; n=2, a(2)=163; n=3, a(3)=244
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CROSSREFS
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Cf. A031433, A010734
Sequence in context: A039547 A044252 A044633 this_sequence A044414 A044795 A092229
Adjacent sequences: A158120 A158121 A158122 this_sequence A158124 A158125 A158126
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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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