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Search: id:A113123
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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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+0
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; listen)
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OFFSET
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1,3
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COMMENT
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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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LINKS
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Leroy Quet, Home Page (listed in lieu of email address)
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EXAMPLE
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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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PROGRAM
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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
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Cf. A100398, A055573, A113124.
Sequence in context: A133922 A088139 A152556 this_sequence A076615 A098777 A127226
Adjacent sequences: A113120 A113121 A113122 this_sequence A113124 A113125 A113126
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KEYWORD
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easy,frac,nonn
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AUTHOR
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Leroy Quet Oct 14 2005
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EXTENSIONS
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More terms from Joshua Zucker (joshua.zucker(AT)stanfordalumni.org), May 08 2006
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