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 A227634 #11 Sep 17 2013 06:00:47
%S A227634 1,1,3,2,3,5,1,6,4,3,5,2,5,3,4,5,6,10,18,1,11,8,6,5,4,7,10,3,5,7,9,15,
%T A227634 2,11,7,5,8,14,3,10,7,4,9,5,11,6,7,8,10,12,15,21,34,1,40,24,17,13,11,
%U A227634 10,8,7,13,6,11,5,14,9,17,4,11,7,10,13,22,3,17
%N A227634 Least splitter of log(n) and log(n+1).
%C A227634 Essentially the same as A183163. - _R. J. Mathar_, Jul 27 2013
%C A227634 Suppose that x < y. The least splitter of x and y is introduced at A227631 as the least positive integer d such that x <= c/d < y for some integer c; the number c/d is called the least splitting rational of x and y.
%H A227634 Clark Kimberling, <a href="/A227634/b227634.txt">Table of n, a(n) for n = 1..1000</a>
%e A227634 The splitting rationals of consecutive numbers log(1), log(2), ... are 0, 1, 4/3, 3/2, 5/3, 9/5, 2, 13/6, 9/4, 7/3, 12/5, 5/2, 13/5; the denominators form A227634, and the numerators, A227684. Chain:
%e A227634 log(1) <= 0 < log(2) < 1 < log(3) < 4/3 < log(4) < 3/2 < log(5) < 5/3 < ...
%t A227634 h[n_] := h[n] = HarmonicNumber[n]; r[x_, y_] := Module[{c, d}, d = NestWhile[#1 + 1 &, 1, ! (c = Ceiling[#1 x - 1]) < Ceiling[#1 y] - 1 &]; (c + 1)/d]; t = Table[r[Log[n], Log[n + 1]], {n, 1, 120}] (*fractions*)
%t A227634 Denominator[t] (* A227634 *)
%t A227634 Numerator[t] (* A227684 *)
%Y A227634 Cf. A227631.
%K A227634 nonn,frac,easy
%O A227634 1,3
%A A227634 _Clark Kimberling_, Jul 18 2013