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Search: id:A157843
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| A157843 |
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a(n)=1728000*n-1343760 (n>0) |
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+0
3
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| 384240, 2112240, 3840240, 5568240, 7296240, 9024240, 10752240, 12480240, 14208240, 15936240, 17664240, 19392240, 21120240, 22848240, 24576240, 26304240, 28032240, 29760240, 31488240, 33216240, 34944240, 36672240
(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=[A157842] 3600*n.^2-5599*n +2177 (178, 5379, 17780,.,); Y=[A157843] 1728000*n - 1343760 (384240, 2112240..,); X=[A157844] 103680000*n^2-161251200*n +62697601 (5126401, 154915201,.,), we have, for all terms, Pell's equation X^2-A*Y^2=1. Example: 5126401^2-178 *384240^2=1; 154915201^2-5379*2112240^2=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)=1728000*n-1343760 (n>0)
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EXAMPLE
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For n=1, a(1)=384240; n=2, a(2)=2112240; n=3, a(3)=3840240
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CROSSREFS
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Cf. A157842, A157844
Sequence in context: A133978 A159265 A133976 this_sequence A157739 A106778 A165959
Adjacent sequences: A157840 A157841 A157842 this_sequence A157844 A157845 A157846
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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 07 2009
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