This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A113123 #16 Mar 31 2017 02:56:16
%S A113123 0,1,2,2,16,22,70,106,1836,2639,14281,21167,167857,87932,169452,
%T A113123 923889,3590229,950596,40366604,23213361,517630,1391957,160363133,
%U A113123 222528683,10125035246,4324958013,81828906108,71315450571,4320297286472
%N A113123 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.
%C A113123 A100398 gives terms of continued fractions of harmonic numbers.
%C A113123 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
%e A113123 H(6) = 49/20 = 2 +1/(2 +1/(4 +1/2)), so a(6) = numerator of 2 +1/(2 +1/4) = 22/9.
%o A113123 (PLT Scheme) ;;(harmonic n) is the n-th harmonic sum
%o A113123 ;;frac->cf and cf->frac are utility functions that convert fractions to continued fractions and vice versa.
%o A113123 (define (A113123 n)
%o A113123 (cond
%o A113123 [(= n 1) 0]
%o A113123 [else (numerator (cf->frac (reverse (rest (reverse (frac->cf (harmonic n)))))))]))
%o A113123 ;; _Joshua Zucker_, May 08 2006
%Y A113123 Cf. A100398, A055573, A113124.
%K A113123 easy,frac,nonn
%O A113123 1,3
%A A113123 _Leroy Quet_, Oct 14 2005
%E A113123 More terms from _Joshua Zucker_, May 08 2006