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A081460
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Consider the mapping f(r) = (1/2)*(r + N/r) from rationals to rationals where N = 5. Starting with a = 2 and applying the mapping to each new (reduced) rational number gives 2, 9/4, 161/72, 51841/23184, ..., tending to N^(1/2). Sequence gives values of the denominators.
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3
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1, 4, 72, 23184, 2403763488, 25840354427429161536, 2986152136938872067784669198846010266752, 39878504028822311675150039382403961856254569551519724209276629577579916539865344
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Related sequence pairs (numerator, denominator) can be obtained by choosing N = 2, 3, 6 etc.
The sequence satisfies the Pell equation A081459(n+1)^2 - 5*a(n+1)^2 = 1. - Vincenzo Librandi, Dec 20 2011
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 1..11
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FORMULA
| a(n) = 2*a(n-1)*A081459(n-1). - Mario Catalani (mario.catalani(AT)unito.it), May 21 2003
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PROG
| (PARI) {r=2; N=5; for(n=1, 8, a=numerator(r); b=denominator(r); print1(b, ", "); r=(1/2)*(r + N/r))}
(MAGMA) m:=8; f:=[ n eq 1 select 2 else (Self(n-1)+5/Self(n-1))/2: n in [1..m] ]; [ Denominator(f[n]): n in [1..m] ]; // Bruno Berselli, Dec 20 2011
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CROSSREFS
| Cf. A000129, A001333, A081459.
Sequence in context: A152653 A172478 A087315 * A055556 A168299 A089665
Adjacent sequences: A081457 A081458 A081459 * A081461 A081462 A081463
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KEYWORD
| nonn
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AUTHOR
| Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Mar 22 2003
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EXTENSIONS
| Edited and extended by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de) and Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Apr 06 2003
a(8) corrected by Vincenzo Librandi, Dec 20 2011
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