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Search: id:A158128
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| 101, 201, 301, 401, 501, 601, 701, 801, 901, 1001, 1101, 1201, 1301, 1401, 1501, 1601, 1701, 1801, 1901, 2001, 2101, 2201, 2301, 2401, 2501, 2601, 2701, 2801, 2901, 3001, 3101, 3201, 3301, 3401, 3501, 3601, 3701, 3801, 3901, 4001, 4101, 4201, 4301, 4401
(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=[A158127] 100*n.^2+2*n (n>0, 102, 404, 906,.,. ,.,); Y=[A010692] 10 (10, 10, 10,.,); X=[A158128] 100*n+1 (n>0, 101, 201, 301, ,. .,), we have, for all terms, Pell's equation X^2-A*Y^2=1. Example: 101^2-102*10^2=1; 201^2-404*10^2=1; 301^2-906*10^2=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)=100*n+1 (n>0)
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EXAMPLE
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For n=1 a(1)=101; n=2, a(2)=201; n03, a(3)=301
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CROSSREFS
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Cf. A158127, A010692
Sequence in context: A100775 A044333 A044714 this_sequence A162670 A134970 A081365
Adjacent sequences: A158125 A158126 A158127 this_sequence A158129 A158130 A158131
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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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