OFFSET
1,1
COMMENTS
For n > 1, these are the numbers u for which [hm(1,2,...,u)] > [hm(1,2,...,u-1)], where [ ] = floor and hm = harmonic mean; for n>=1, they are the numbers k such that mean(1,1/2,...,1/k) <= 1/n < mean(1,1/2,...,1/(k-1)).
LINKS
Clark Kimberling, Table of n, a(n) for n = 1..10000
MATHEMATICA
(* first, for arithmetic means *)
t = 0; m = 1; Table[t = NestWhile[# + 1 &, t + 1, (m = ((# - 1) m + 1/(#))/(#)) >= 1/n &], {n, 1, 100}] (* Peter J. C. Moses, Jul 10 2013 *)
(* next, for harmonic means *)
t = Select[Range[2, 1000], Floor[#/HarmonicNumber[#]] > Floor[(# -1)/HarmonicNumber[# - 1]] &[N[#, 50]] &] (* Peter J. C. Moses, Jul 10 2013 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Clark Kimberling, Oct 21 2003
EXTENSIONS
Simpler definition and editing by Clark Kimberling, Jul 11 2013
STATUS
approved