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A113124
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.
2
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
OFFSET
1,5
COMMENTS
A100398 gives terms of continued fractions of harmonic numbers.
EXAMPLE
H(6) = 49/20 = 2 +1/(2 +1/(4 +1/2)), so a(6) = denominator of 2 +1/(2 +1/4) = 22/9.
PROG
(PLT Scheme) ;; (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)))))))])) ;; Joshua Zucker, May 08 2006
CROSSREFS
KEYWORD
easy,frac,nonn
AUTHOR
Leroy Quet, Oct 14 2005
EXTENSIONS
More terms from Joshua Zucker, May 08 2006
STATUS
approved