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Search: id:A158071
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| 65, 129, 193, 257, 321, 385, 449, 513, 577, 641, 705, 769, 833, 897, 961, 1025, 1089, 1153, 1217, 1281, 1345, 1409, 1473, 1537, 1601, 1665, 1729, 1793, 1857, 1921, 1985, 2049, 2113, 2177, 2241, 2305, 2369, 2433, 2497, 2561, 2625, 2689, 2753, 2817, 2881
(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=[A158070] 64*n.^2+2*n (n>0, 66, 260, 582,.,. ,.,); Y=[A010731] 8 (8,8,8,.,..,); X=[A158071] 64*n+1 (n>0, 65, 129, 193, ,. .,), we have, for all terms, Pell's equation X^2-A*Y^2=1. Example: 65^2-66*8^2=1; 129^2-260*8^2=1; 193^2-582*8^2=1.
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LINKS
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Wolfram MathWorld, Pell Equation
Vincenzo Librandi, X^2-AY^2=1
Edward Everett Withford, Pell Equation
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FORMULA
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a(n)=64*n+1 ((n>0)
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EXAMPLE
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For n=1, a(1)=65; n=2, a(2)=129; n=3, a(3)=193
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CROSSREFS
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Cf. A158070, A010731
Sequence in context: A118159 A044188 A044569 this_sequence A073631 A092226 A121944
Adjacent sequences: A158068 A158069 A158070 this_sequence A158072 A158073 A158074
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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 12 2009
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