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Search: id:A157739
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| A157739 |
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a(n)=388962*n^2-1764*n+1 (n>0) |
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+0
3
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| 387199, 1552321, 3495367, 6216337, 9715231, 13992049, 19046791, 24879457, 31490047, 38878561, 47044999, 55989361, 65711647, 76211857, 87489991, 99546049, 112380031, 125991937, 140381767, 155549521, 171495199, 188218801
(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=[A157737] 441*n.^2-2*n (439, 1760, 3963,..,); Y=[A157738] 18522*n- 42 (18480, 37002, 55524..,); X=[A157739] 388962*n^2-1764*n +1 (387199, 1552321, 3495367,..,), we have, for all terms, Pell's equation X^2-A*Y^2=1. Example: 387199^2-439 *18480^2=1; 1552321^2-1760*37002^2=1; 3495367^2-3963*55524^2=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)=388962*n^2-1764*n+1 (n>0)
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EXAMPLE
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For n=1, a(1)=387199; n=2, a(2)=1552321; n=3, a(3)=3495367
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CROSSREFS
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Cf. A157737, A157738
Sequence in context: A159265 A133976 A157843 this_sequence A106778 A165959 A016820
Adjacent sequences: A157736 A157737 A157738 this_sequence A157740 A157741 A157742
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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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