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Search: id:A157951
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| 129, 257, 385, 513, 641, 769, 897, 1025, 1153, 1281, 1409, 1537, 1665, 1793, 1921, 2049, 2177, 2305, 2433, 2561, 2689, 2817, 2945, 3073, 3201, 3329, 3457, 3585, 3713, 3841, 3969, 4097, 4225, 4353, 4481, 4609, 4737, 4865, 4993, 5121, 5249, 5377, 5505
(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=[A031694] 64*n.^2+n (65, 258, 579,.,); Y=[A010855] 16 (16, 16, 16, ,.,); X=[A157951] 128*n+1 (129, 257, 385.,), we have, for all terms, Pell's equation X^2-A*Y^2=1. Example: 129^2-65 *16^2=1; 257^2-258*16^2=1; 385^2-579*16^2=1.
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LINKS
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Edward Everett Withford, Pell Equation
Wolfram MathWorld, Pell Equation
Vincenzo Librandi, X^2-AY^2=1
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FORMULA
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a(n)=128*n+1 (n>0)
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EXAMPLE
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For n=1, a(1)=129; n=2, a(2)=257; n=3, a(3)=385
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CROSSREFS
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Cf. A031694, A010855
Sequence in context: A060878 A127337 A034072 this_sequence A043383 A036548 A046286
Adjacent sequences: A157948 A157949 A157950 this_sequence A157952 A157953 A157954
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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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