A227779 Least splitter of s(n) and s(n+1), where s(n) = sum{(k + 1/2)^(-1/2), k >= 1}.

1, 2, 1, 2, 1, 2, 3, 1, 2, 3, 1, 3, 2, 4, 1, 3, 2, 4, 1, 3, 2, 3, 5, 1, 3, 2, 3, 5, 1, 4, 3, 2, 3, 6, 1, 4, 3, 2, 3, 5, 1, 5, 3, 2, 3, 4, 7, 1, 4, 3, 2, 3, 4, 6, 1, 5, 3, 5, 2, 3, 4, 7, 1, 5, 3, 5, 2, 3, 4, 6, 1, 6, 4, 3, 2, 5, 3, 5, 8, 1, 5, 4, 3, 2, 5, 3

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. It appears that d=1 (i.e., c/d is an integer) for rationals c/d in positions given by A024206.

Links

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

Example

The first 15 splitting rationals are 1, 3/2, 2, 5/2, 3, 7/2, 11/3, 4, 9/2, 14/3, 5, 16/3, 11/2, 23/4, 6.

Mathematica

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] = Sum[(k + 1/2)^(-1/2), {k, 1, n}]; t = Table[r[s[n], s[n + 1]], {n, 1, 220}]; Denominator[t] (* Peter J. C. Moses, Jul 15 2013 *)

Crossrefs

Cf. A227631.

Sequence in context: A023118 A122197 A030718 * A194066 A308916 A353171

Adjacent sequences: A227776 A227777 A227778 * A227780 A227781 A227782

Keyword

nonn,frac,easy

Author

Clark Kimberling, Jul 30 2013

Status

approved