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Search: id:A157362
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| 47, 192, 435, 776, 1215, 1752, 2387, 3120, 3951, 4880, 5907, 7032, 8255, 9576, 10995, 12512, 14127, 15840, 17651, 19560, 21567, 23672, 25875, 28176, 30575, 33072, 35667, 38360, 41151, 44040, 47027, 50112, 53295, 56576, 59955, 63432, 67007
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OFFSET
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1,1
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COMMENT
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If A=[A157362] 49*n.^2-2*n (47,192,435,776,...,); Y=[A157363] 686*n-14 (672, 1358, 2044, 2730,...,); X=[A157364] 4802*n^2-196*n+1 (4607,18817,42631,76049,...,) ; , we have for all terms, Pell's equation X^2-A*Y^2=1. Example: 4607^2-47*672^2=1; 18817^2-192*1358^2=1; 42631^2-435*2044^2=1; 76049^2-776*2730^2=1.
If A=[A157362] 49*n.^2-2*n (n>0, 47, 192, 435,.,. ,.,); Y=[A010727] 7 (7,7,7,.,.,); X=[A044567] 49*n-1 (n>0, 48, 97, 146, ,. .,), we have, for all terms, Pell's equation X^2-A*Y^2=1. Example: 48^2-47*7^2=1; 97^2-192*7^2=1; 146^2-435*7^2=1. [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Mar 12 2009]
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LINKS
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Vincenzo Librandi, X^2-AY^2=1
Edward Everett Withford, Pell Equation [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Mar 12 2009]
Wolfram MathWorld, Pell Equation [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Mar 12 2009]
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FORMULA
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a(n)=49*n^2-2*n (n>0)
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EXAMPLE
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For n=1, a(1)=47, n=2, a(2)=192; n=3, a(3)=435
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CROSSREFS
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Cf. A157363, A157364
Cf. A010727, A044567 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Mar 12 2009]
Sequence in context: A158632 A142413 A065532 this_sequence A141874 A142203 A067986
Adjacent sequences: A157359 A157360 A157361 this_sequence A157363 A157364 A157365
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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), Feb 28 2009
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