OFFSET
4,8
COMMENTS
For k = 1..20, the runlength of k's is given by 7, 11, 14, 18, 21, 25, 29, 32, 36, 39, 42, 47, 50, 53, 57, 61, 64, 67, 72, 74.
LINKS
Clark Kimberling, Table of n, a(n) for n = 4..1000
FORMULA
a(n) = Sum_{k>=1} sign(1 - sign(2*H_k - H_n)). - Mats Granvik, Apr 06 2021
EXAMPLE
1/3 + 1/4 + ... + 1/10 < 1 + 1/2 < 1/3 + 1/4 + ... + 1/11, so that a(11) = 2.
MATHEMATICA
(* first program *)
h[n_] := HarmonicNumber[n]; f[n_, k_] := f[n, k] = If[2 h[k] <= h[n] && 2 h[k + 1] > h[n], 1, 0]; t[n_] := t[n] = Table[f[n, k], {k, 1, n}]; a[n_] := First[Position[t[n], 1]]; u = Flatten[Table[a[n], {n, 4, 500}]]
(* second program, with plot *)
a[1] = 0; a[n_] := a[n] = NestWhile[# + 1 &, a[n - 1] + 1, Sum[1/k, {k, 1, #}] < Sum[1/k, {k, # + 1, n}] &] - 1; A226764 = Map[a, Range[4, 500]]; ListLogLogPlot[A226764] (* Peter J. C. Moses, Jun 20 2013 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Clark Kimberling, Jun 19 2013
STATUS
approved