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Search: id:A114046
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| A114046 |
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Numbers x such that x^2 - 92*y^2 = 1. |
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+0
1
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| 1, 1151, 2649601, 6099380351, 14040770918401, 32321848554778751, 74404881332329766401, 171280004505174567476351, 394286495966030522000793601, 907647342433797756471259393151
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Quote from the link prompting this sequence. A person who can, within a year, solve x^2 - 92y^2 = 1 is a mathematician. Brahmagupta [598-668] This sequence is computed with g(1e9,92) in the pari program.
A Pell equation - Benoit Cloitre (benoit7848c(AT)orange.fr), Feb 03 2006
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LINKS
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Author?, Title?
Tanya Khovanova, Recursive Sequences
John Robertson, Home page.
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FORMULA
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a(0)=1, a(1)=1151 then a(n)=2302*a(n-1)-a(n-2) - Benoit Cloitre (benoit7848c(AT)orange.fr), Feb 03 2006
G.f.: (1-1151x)/(1-2302x+x^2). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 18 2008]
a(n)=1/2*{[1151-240*sqrt(23)]^n+[1151+240*sqrt(23)]^n}, with n>=0 [From Paolo P. Lava (ppl(AT)spl.at), Nov 24 2008]
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EXAMPLE
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(1151^2 - 1)/92 = 120^2.
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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=1151; for(n=2, 30, a2=2302*a1-a0; a0=a1; a1=a2; print1(a2, ", ")) (Cloitre)
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CROSSREFS
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Sequence in context: A086259 A098976 A154374 this_sequence A035888 A131527 A170775
Adjacent sequences: A114043 A114044 A114045 this_sequence A114047 A114048 A114049
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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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