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Search: id:A113124
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| A113124 |
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Denominator of next-best approximation to harmonic numbers. a(n) = Denominator 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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| 1, 1, 1, 1, 7, 9, 27, 39, 649, 901, 4729, 6821, 52783, 27043, 51067, 273281, 1043807, 271979, 11378119, 6452207, 141997, 377141, 42943389, 58933037, 2653340203, 1122077597, 21027833867, 18159496967, 1090528730477, 236529224117
(list; graph; listen)
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OFFSET
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1,5
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COMMENT
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A100398 gives terms of continued fractions of harmonic numbers.
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EXAMPLE
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H(6) = 49/20 = 2 +1/(2 +1/(4 +1/2)), so a(6) = denominator 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 (A113124 n)
(cond
[(= n 1) 1]
[else (denominator (cf->frac (reverse (rest (reverse (frac->cf (harmonic n)))))))]))
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CROSSREFS
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Cf. A100398, A055573, A113123.
Sequence in context: A125260 A104703 A032617 this_sequence A030404 A066930 A085903
Adjacent sequences: A113121 A113122 A113123 this_sequence A113125 A113126 A113127
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KEYWORD
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easy,frac,nonn
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AUTHOR
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Leroy Quet (qq-quet(AT)mindspring.com), 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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