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Search: id:A114049
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| A114049 |
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x such that x^2 - 21*y^2 = 1. |
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+0
1
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| 1, 55, 6049, 665335, 73180801, 8049222775, 885341324449, 97379496466615, 10710859270003201, 1178097140203885495, 129579974563157401249, 14252619104807110251895, 1567658521554218970307201
(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(1e9,21) in the Pari program.
A Pellian 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)=55 then a(n)=110*a(n-1)-a(n-2) - Benoit Cloitre (benoit7848c(AT)orange.fr), Feb 03 2006
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EXAMPLE
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(55^2-1)/21 = 12^2
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MATHEMATICA
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Table[ Numerator@ FromContinuedFraction@ ContinuedFraction[Sqrt@21, Length@ Last@ ContinuedFraction@ Sqrt@21*n], {n, 12}] (from Robert G. Wilson v (rgwv(at)rgwv.com), Feb 28 2006)
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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=55; for(n=2, 30, a2=110*a1-a0; a0=a1; a1=a2; print1(a2, ", ")) (Cloitre)
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CROSSREFS
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Sequence in context: A037156 A116110 A060204 this_sequence A028471 A004708 A090813
Adjacent sequences: A114046 A114047 A114048 this_sequence A114050 A114051 A114052
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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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