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Search: id:A114047
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| A114047 |
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x such that x^2 - 13*y^2 = 1. |
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+0
1
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| 1, 649, 842401, 1093435849, 1419278889601, 1842222905266249, 2391203911756701601, 3103780835237293411849, 4028705132934095091878401, 5229256158767620191964752649, 6787570465375238075075157060001
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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This sequence is computed with g(1e9,13) in the pari program.
A pellian equation (Pell's equation) - Benoit Cloitre (benoit7848c(AT)orange.fr), Feb 03 2006
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LINKS
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Tanya Khovanova, Recursive Sequences
Author?, Title?
John Robertson, Home page.
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FORMULA
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a(0)=1, a(1)=649 then a(n)=1298*a(n-1)-a(n-2) - Benoit Cloitre (benoit7848c(AT)orange.fr), Feb 03 2006
G.f.: (1-649x)/(1-1298x+x^2). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 18 2008]
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EXAMPLE
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(649^2-1)/13 = 180^2
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PROGRAM
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(PARI) g(n, k) = for(y=0, n, x=k*y^2+1; if(issquare(x), print1(floor(sqrt(x))", ")))
(PARI) a0=1; a1=649; for(n=2, 30, a2=1298*a1-a0; a0=a1; a1=a2; print1(a2, ", ")) (Cloitre)
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CROSSREFS
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Sequence in context: A035755 A107551 A154358 this_sequence A157915 A158639 A162025
Adjacent sequences: A114044 A114045 A114046 this_sequence A114048 A114049 A114050
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KEYWORD
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easy,nonn
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AUTHOR
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Cino Hilliard (hillcino368(AT)gmail.com), Feb 01 2006
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EXTENSIONS
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More terms from Benoit Cloitre (benoit7848c(AT)orange.fr), Feb 03 2006
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