A227803 Least splitter of s(n) and s(n+1), where s(n) = (1 - 1/n)^n.

1, 4, 10, 22, 3, 53, 35, 26, 23, 20, 37, 17, 48, 31, 45, 73, 14, 95, 67, 53, 39, 64, 25, 111, 61, 97, 36, 119, 83, 47, 105, 58, 69, 80, 91, 102, 124, 146, 179, 234, 322, 509, 11, 778, 448, 316, 250, 206, 173, 151, 140, 129, 118, 107, 203, 96, 181, 85, 159

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) -> 1/e, the sequence of least splitting rationals also approaches 1/e .

Links

Clark Kimberling, Table of n, a(n) for n = 1..1000

Example

The first 15 splitting rationals are 0/1, 1/4, 3/10, 7/22, 1/3, 18/53, 12/35, 9/26, 8/23, 7/20, 13/37, 6/17, 17/48, 11/31, 16/45.

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}]; Denominator[t] (* A227803, Peter J. C. Moses, Jul 15 2013 *)

Crossrefs

Cf. A227631, A225594.

Sequence in context: A329361 A290998 A369846 * A109885 A054211 A112770

Adjacent sequences: A227800 A227801 A227802 * A227804 A227805 A227806

Keyword

nonn,frac,easy

Author

Clark Kimberling, Jul 31 2013

Status

approved