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Search: id:A158447
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| 9, 39, 89, 159, 249, 359, 489, 639, 809, 999, 1209, 1439, 1689, 1959, 2249, 2559, 2889, 3239, 3609, 3999, 4409, 4839, 5289, 5759, 6249, 6759, 7289, 7839, 8409, 8999, 9609, 10239, 10889, 11559, 12249, 12959, 13689, 14439, 15209, 15999, 16809, 17639
(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=[A158446] 25*n.^2-5 (n>0, 20, 95, 220,.,); Y=[A005843] 2*n (n>0, 2, 4, 6,.,); X = [A158447] 10*n^2-1 (n>0, 9, 39, 89, .,), we have, for all terms, Pell's equation X^2-A*Y^2=1. Example: 9^2-20*2^2=1; 39^2-95*4^2=1; 89^2-220*6^2=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)=10*n^2-1 (n>0)
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EXAMPLE
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For n=1, a(1)=9; n=2, a(2)=39; n=3, a(3)=89
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CROSSREFS
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Cf. A005843, A158446
Sequence in context: A071229 A071238 A050854 this_sequence A023163 A054121 A139594
Adjacent sequences: A158444 A158445 A158446 this_sequence A158448 A158449 A158450
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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 19 2009
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