login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A227684 Numerator of least splitting rational of log(n) and log(n+1). 2
0, 1, 4, 3, 5, 9, 2, 13, 9, 7, 12, 5, 13, 8, 11, 14, 17, 29, 53, 3, 34, 25, 19, 16, 13, 23, 33, 10, 17, 24, 31, 52, 7, 39, 25, 18, 29, 51, 11, 37, 26, 15, 34, 19, 42, 23, 27, 31, 39, 47, 59, 83, 135, 4, 161, 97, 69, 53, 45, 41, 33, 29, 54, 25, 46, 21, 59, 38 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

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.

LINKS

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

EXAMPLE

The splitting rationals of consecutive numbers log(1), log(2), ... are 0, 1, 4/3, 3/2, 5/3, 9/5, 2, 13/6, 9/4, 7/3, 12/5, 5/2, 13/5; the denominators form A227634, and the numerators, A227684.  Chain:

log(1) <= 0 < log(2) < 1 < log(3) < 4/3 < log(4) < 3/2 < log(5) < 5/3 < ...

MATHEMATICA

h[n_] := h[n] = HarmonicNumber[n]; r[x_, y_] := Module[{c, d}, d = NestWhile[#1 + 1 &, 1, ! (c = Ceiling[#1 x - 1]) < Ceiling[#1 y] - 1 &]; (c + 1)/d]; t = Table[r[Log[n], Log[n + 1]], {n, 1, 120}] (*fractions*)

Denominator[t] (* A227634 *)

Numerator[t]  (* A227684 *)

CROSSREFS

Cf. A227631, A227634.

Sequence in context: A256367 A242910 A200350 * A200636 A229938 A226654

Adjacent sequences:  A227681 A227682 A227683 * A227685 A227686 A227687

KEYWORD

nonn,frac,easy

AUTHOR

Clark Kimberling, Jul 19 2013

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified November 20 17:09 EST 2019. Contains 329337 sequences. (Running on oeis4.)