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Search: id:A157727
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| A157727 |
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a(n)=15625*n^2-2136*n+73 (n>0) |
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+0
3
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| 13562, 58301, 134290, 241529, 380018, 549757, 750746, 982985, 1246474, 1541213, 1867202, 2224441, 2612930, 3032669, 3483658, 3965897, 4479386, 5024125, 5600114, 6207353, 6845842, 7515581, 8216570, 8948809, 9712298, 10507037
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OFFSET
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1,1
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COMMENT
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If A=[A157727] 15625*n.^2-2136*n+73 (13562, 58301, 134290, ,..,); Y=[A157728] 3906250*n- 267000 (3639250, 7545500,..,); X=[A157729] 488281250*n^2-66750000*n + 2281249 (423812499, 1821906249,..,), we have, for all terms, Pell's equation X^2-A*Y^2=1. Example: 423812499^2-13562*3639250^2=1; 1821906249^2-58301*7545500^2=1.
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LINKS
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Vincenzo Librandi, X^2-AY^2=1
Edward Everett Withford, Pell Equation
Wolfram MathWorld, Pell Equation
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FORMULA
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a(n)=15625*n^2-2136*n+73 (n>0)
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EXAMPLE
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For n=1, a(1)=13562; n=2, a(2)=58301; n=3, a(3)=134290
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CROSSREFS
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Cf. A157728, A157729
Sequence in context: A029557 A115922 A064981 this_sequence A108418 A088870 A047827
Adjacent sequences: A157724 A157725 A157726 this_sequence A157728 A157729 A157730
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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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