cp's OEIS Frontend

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.

%I A113124 #14 Mar 31 2017 02:56:19
%S A113124 1,1,1,1,7,9,27,39,649,901,4729,6821,52783,27043,51067,273281,1043807,
%T A113124 271979,11378119,6452207,141997,377141,42943389,58933037,2653340203,
%U A113124 1122077597,21027833867,18159496967,1090528730477,236529224117
%N 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.
%C A113124 A100398 gives terms of continued fractions of harmonic numbers.
%e A113124 H(6) = 49/20 = 2 +1/(2 +1/(4 +1/2)), so a(6) = denominator of 2 +1/(2 +1/4) = 22/9.
%o A113124 (PLT Scheme) ;;(harmonic n) is the n-th harmonic sum
%o A113124 ;;frac->cf and cf->frac are utility functions that convert fractions to continued fractions and vice versa.
%o A113124 (define (A113124 n)
%o A113124 (cond
%o A113124 [(= n 1) 1]
%o A113124 [else (denominator (cf->frac (reverse (rest (reverse (frac->cf (harmonic n)))))))])) ;; _Joshua Zucker_, May 08 2006
%Y A113124 Cf. A100398, A055573, A113123.
%K A113124 easy,frac,nonn
%O A113124 1,5
%A A113124 _Leroy Quet_, Oct 14 2005
%E A113124 More terms from _Joshua Zucker_, May 08 2006