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Search: id:A114048
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| A114048 |
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x such that x^2 - 19*y^2 = 1. |
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+0
1
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| 1, 170, 57799, 19651490, 6681448801, 2271672940850, 772362118440199, 262600848596726810, 89283516160768675201, 30356132893812752841530, 10320995900380175197444999, 3509108249996365754378458130
(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(1e9,19) 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)=170 then a(n)=340*a(n-1)-a(n-2) - Benoit Cloitre (benoit7848c(AT)orange.fr), Feb 03 2006
G.f.: (1-170x)/(1-340x+x^2). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 18 2008]
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EXAMPLE
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(170^2-1)/19 = 39^2
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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) a(n)=real((170+39*quadgen(4*19))^n) /* Michael Somos Feb 15 2006 */
(PARI) a0=1; a1=170; for(n=2, 30, a2=340*a1-a0; a0=a1; a1=a2; print1(a2, ", ")) (Cloitre)
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CROSSREFS
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Sequence in context: A031704 A133328 A098244 this_sequence A015975 A045149 A031511
Adjacent sequences: A114045 A114046 A114047 this_sequence A114049 A114050 A114051
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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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