A227778 Least splitter of n-th and (n+1)st partial sums of 1/1 + 1/3 + ... + 1/(2n-1).

1, 2, 3, 4, 5, 9, 1, 13, 8, 6, 5, 4, 7, 3, 11, 8, 5, 7, 11, 2, 19, 11, 9, 7, 5, 8, 11, 20, 3, 13, 7, 11, 15, 4, 13, 9, 5, 16, 11, 6, 13, 7, 15, 8, 9, 10, 11, 13, 14, 17, 20, 24, 31, 43, 69, 1, 84, 49, 35, 27, 23, 19, 17, 15, 14, 12, 11, 21, 10, 9, 17, 8, 15

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. It appears that c/d is an integer (i.e., d = 1) for rationals in positions given by A082315; e.g. 1, 7, 56, ...

Examples

			The first 15 splitting rationals are 1/1, 3/2, 5/3, 7/4, 9/5, 17/9, 2/1, 27/13, 17/8, 13/6, 11/5, 9/4, 16/7, 7/3, 26/11.
		

Links

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

Crossrefs

Cf. A227631.

Programs

Mathematica

z = 16; r[x_, y_] := Module[{a, b, x1 = Min[{x, y}], y1 = Max[{x, y}]}, If[x == y, x, b = NestWhile[#1 + 1 &, 1, ! (a = Ceiling[#1 x1 - 1]) < Ceiling[#1 y1] - 1 &]; (a + 1)/b]]; s[n_] := s[n] = Sum[1/(k - 1)!, {k, 1, n}]; N[Table[s[k], {k, 1, z}]]; t = Table[r[s[n], s[n + 1]], {n, 2, z}]; Denominator[t] (* Peter J. C. Moses, Jul 15 2013 *)