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Search: id:A157732
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| A157732 |
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a(n)=388962*n^2-430416*n+119071 (n>0) |
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+0
3
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| 77617, 814087, 2328481, 4620799, 7691041, 11539207, 16165297, 21569311, 27751249, 34711111, 42448897, 50964607, 60258241, 70329799, 81179281, 92806687, 105212017, 118395271, 132356449, 147095551, 162612577, 178907527
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OFFSET
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1,1
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COMMENT
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If A=[A157730] 441*n.^2-488*n+135 (88, 923, 2640, 5239,..,); Y=[A157731] 18522*n- 10248 (8274, 26796, 45318..,); X=[A157732] 388962*n^2-430416*n + 119071 (77617, 814087, 2328481,..,), we have, for all terms, Pell's equation X^2-A*Y^2=1. Example: 77617^2-88 * 8274^2=1; 814087^2-923*26796^2=1; 2328481^2-2640*45318^2=1.
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LINKS
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Edward Everett Withford, Pell Equation
Vincenzo Librandi, X^2-AY^2=1
Philippe Chevanne, Pell Equation
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FORMULA
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a(n)=388962*n^2-430416*n+119071 (n>0)
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EXAMPLE
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For n=1, a(1)=77617; n=2, a(2)=814087; n=3, a(3)=2328481
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CROSSREFS
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Cf. A157730, A157731
Sequence in context: A046720 A152498 A124489 this_sequence A069044 A087026 A133971
Adjacent sequences: A157729 A157730 A157731 this_sequence A157733 A157734 A157735
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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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