A225594 Least splitter of s(n) and s(n+1), where s(n) = (1 + n)^(1/n).

1, 3, 5, 9, 2, 11, 9, 7, 12, 5, 18, 13, 8, 19, 11, 25, 14, 17, 23, 26, 35, 44, 65, 116, 3, 115, 73, 55, 46, 37, 34, 31, 28, 25, 47, 22, 41, 19, 73, 35, 51, 83, 16, 61, 45, 29, 42, 55, 68, 107, 13, 101, 75, 49, 85, 36, 59, 105, 23, 79, 56, 33, 109, 76, 43, 53

Offset: 1

Author

Clark Kimberling, Jul 30 2013

Keywords

• nonn
• frac
• easy

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.

Examples

			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.
		

Links

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

Crossrefs

Cf. A227631.

Programs

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 *)