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A113123
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Numerator of next-best approximation to harmonic numbers. a(n) = Numerator of (A055573(n)-1)th convergent of n-th harmonic number, sum{k=1..n}1/k.
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2
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0, 1, 2, 2, 16, 22, 70, 106, 1836, 2639, 14281, 21167, 167857, 87932, 169452, 923889, 3590229, 950596, 40366604, 23213361, 517630, 1391957, 160363133, 222528683, 10125035246, 4324958013, 81828906108, 71315450571, 4320297286472
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| A100398 gives terms of continued fractions of harmonic numbers.
For n >= 2, a(n) = the denominator of the ratio equal to the continued fraction made by reversing the order of the terms of the continued fraction of the n-th harmonic number. (The numerator of this ratio is the numerator of the n-th harmonic number, A001008(n).) - Leroy Quet Dec 24 2006
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EXAMPLE
| H(6) = 49/20 = 2 +1/(2 +1/(4 +1/2)), so a(6) = numerator of 2 +1/(2 +1/4) = 22/9.
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PROG
| PLT DrScheme: - Joshua Zucker (joshua.zucker(AT)stanfordalumni.org), May 08 2006
;; (harmonic n) is the n-th harmonic sum
;; frac->cf and cf->frac are utility functions that convert fractions to continued fractions and vice-versa.
(define (A113123 n)
(cond
[(= n 1) 0]
[else (numerator (cf->frac (reverse (rest (reverse (frac->cf (harmonic n)))))))]))
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CROSSREFS
| Cf. A100398, A055573, A113124.
Sequence in context: A133922 A088139 A152556 * A177832 A076615 A098777
Adjacent sequences: A113120 A113121 A113122 * A113124 A113125 A113126
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KEYWORD
| easy,frac,nonn
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AUTHOR
| Leroy Quet Oct 14 2005
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EXTENSIONS
| More terms from Joshua Zucker (joshua.zucker(AT)stanfordalumni.org), May 08 2006
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