OFFSET
1,2
COMMENTS
See A227631 for the definition of least splitter.
LINKS
Clark Kimberling, Table of n, a(n) for n = 1..1000
EXAMPLE
The first few splitting rationals are 1/1, 3/2, 2/1, 9/4, 7/3, 5/2, 8/3, 11/4, 17/6, 3/1, 31/10, 19/6; e.g. 9/4 splits H(4) and H(5), as indicated by H(4) = 1 + 1/2 + 1/3 + 1/4 = 2.083... < 2.25 < 2.283... = H(5) and the chain H(1) <= 1/1 < H(2) < 3/2 < H(3) < 2/1 < H(4) < 9/4 < ...
MATHEMATICA
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[h[n], h[n + 1]], {n, 1, 120}];
Denominator[t] (* A227629 *)
Numerator[t] (* A227630 *) (* Peter J. C. Moses, Jul 15 2013 *)
CROSSREFS
KEYWORD
nonn,frac
AUTHOR
Clark Kimberling, Jul 18 2013
STATUS
approved