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Search: id:A157741
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| A157741 |
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a(n)=388962*n^2+1764*n+1 (n>0) |
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+0
3
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| 390727, 1559377, 3505951, 6230449, 9732871, 14013217, 19071487, 24907681, 31521799, 38913841, 47083807, 56031697, 65757511, 76261249, 87542911, 99602497, 112440007, 126055441, 140448799, 155620081, 171569287, 188296417
(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=[A031699] 441*n.^2+2*n (443, 1768, 3975,..,); Y=[A157740] 18522*n+ 42 (18564, 37086, 55608..,); X=[A157741] 388962*n^2+1764*n +1 (390727, 1559377, 3505951,..,), we have, for all terms, Pell's equation X^2-A*Y^2=1. Example: 390727^2-443 *18564^2=1; 1559377^2-1768*37086^2=1; 3505951^2-3975*55608^2=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)=388962*n^2+1764*n+1 (n>0)
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EXAMPLE
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For n=1, a(1)=390727; n=2, a(2)=1559377; n=3, a(3)=3505951
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CROSSREFS
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Cf. A031699, A157740
Sequence in context: A017336 A017456 A017588 this_sequence A157623 A145228 A131277
Adjacent sequences: A157738 A157739 A157740 this_sequence A157742 A157743 A157744
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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 05 2009
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