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Search: id:A157731
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| A157731 |
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a(n)=18522*n-10248 (n>0) |
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+0
3
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| 8274, 26796, 45318, 63840, 82362, 100884, 119406, 137928, 156450, 174972, 193494, 212016, 230538, 249060, 267582, 286104, 304626, 323148, 341670, 360192, 378714, 397236, 415758, 434280, 452802, 471324, 489846, 508368, 526890, 545412, 563934
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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
Wolfram MathWorld, Pell Equation
Vincenzo Librandi, X^2-AY^2=1
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FORMULA
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a(n)=18522*n-10248 (n>0)
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EXAMPLE
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For n=1, a(1)=8274; n=2, a(2)=26796; n=3, a(3)=45318
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CROSSREFS
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Cf. A157730, A157732
Sequence in context: A045056 A031850 A166194 this_sequence A064014 A145527 A054215
Adjacent sequences: A157728 A157729 A157730 this_sequence A157732 A157733 A157734
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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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