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Search: id:A157958
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| 243, 485, 727, 969, 1211, 1453, 1695, 1937, 2179, 2421, 2663, 2905, 3147, 3389, 3631, 3873, 4115, 4357, 4599, 4841, 5083, 5325, 5567, 5809, 6051, 6293, 6535, 6777, 7019, 7261, 7503, 7745, 7987, 8229, 8471, 8713, 8955, 9197, 9439, 9681, 9923, 10165
(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=[A031700] 121*n.^2+n (122, 486, 1092,. ,.,); Y=[A010861] 20 (20, 20, 20,..,); X=[A157958] 242*n+1 (243, 485, 727, ,. .,), we have, for all terms, Pell's equation X^2-A*Y^2=1. Example: 243^2-122 *22^2=1; 485^2-486*22^2=1; 727^2-1092*22^2=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)=242*n+1 (n>0)
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EXAMPLE
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For n=1, a(1)=243; n=2, a(2)=485; n=3, a(3)=727
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CROSSREFS
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Cf. A031700, A010861
Adjacent sequences: A157955 A157956 A157957 this_sequence A157959 A157960 A157961
Sequence in context: A018871 A046318 A046375 this_sequence A067838 A113335 A100627
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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 10 2009
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