Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #11 Sep 17 2013 06:00:47
%S 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 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 10,8,7,13,6,11,5,14,9,17,4,11,7,10,13,22,3,17
%N Least splitter of log(n) and log(n+1).
%C Essentially the same as A183163. - _R. J. Mathar_, Jul 27 2013
%C 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 Clark Kimberling, <a href="/A227634/b227634.txt">Table of n, a(n) for n = 1..1000</a>
%e 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 log(1) <= 0 < log(2) < 1 < log(3) < 4/3 < log(4) < 3/2 < log(5) < 5/3 < ...
%t 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 Denominator[t] (* A227634 *)
%t Numerator[t] (* A227684 *)
%Y Cf. A227631.
%K nonn,frac,easy
%O 1,3
%A _Clark Kimberling_, Jul 18 2013