OFFSET
1,2
COMMENTS
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. Since s(n) -> e, the least splitting rationals -> e.
LINKS
Clark Kimberling, Table of n, a(n) for n = 1..1000
EXAMPLE
The first 15 splitting rationals are 2/1, 7/3, 12/5, 22/9, 5/2, 28/11, 23/9, 18/7, 31/12, 13/5, 47/18, 34/13, 21/8, 50/19, 29/11.
MATHEMATICA
z = 100; r[x_, y_] := Module[{c, d}, d = NestWhile[#1 + 1 &, 1, ! (c = Ceiling[#1 x - 1]) < Ceiling[#1 y] - 1 &]; (c + 1)/d]; s[n_] := s[n] = (1 + 1/n)^n; t = Table[r[s[n], s[n + 1]], {n, 1, z}]; fd = Denominator[t] (* Peter J. C. Moses, Jul 15 2013 *)
CROSSREFS
KEYWORD
nonn,frac,easy
AUTHOR
Clark Kimberling, Jul 30 2013
STATUS
approved