A088907 Least k such that mean(1,1/2,...,1/k) <= 1/n.

2, 5, 9, 13, 18, 23, 28, 33, 39, 44, 50, 56, 62, 68, 74, 80, 86, 92, 99, 105, 112, 118, 125, 131, 138, 145, 152, 159, 165, 172, 179, 186, 193, 200, 207, 215, 222, 229, 236, 243, 251, 258, 265, 273, 280, 287, 295, 302, 310, 317, 325, 332, 340, 348, 355, 363

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

Sequence in context: A371730 A055025 A178805 * A130235 A267531 A219647

Adjacent sequences: A088904 A088905 A088906 * A088908 A088909 A088910

Keyword

nonn

Author

Clark Kimberling, Oct 21 2003

Extensions

Simpler definition and editing by Clark Kimberling, Jul 11 2013

Status

approved