A226184 Least positive integer k such that 1 + 1/2 + ... + 1/n < 1/(n+1) + ... + 1/(n+k).

3, 9, 19, 32, 49, 69, 93, 121, 152, 187, 225, 266, 312, 361, 413, 469, 529, 592, 658, 729, 802, 880, 961, 1045, 1133, 1225, 1320, 1419, 1521, 1627, 1736, 1849, 1966, 2086, 2210, 2337, 2468, 2602, 2740, 2882, 3027, 3175, 3327, 3483, 3642, 3805, 3972, 4142

Offset

1,1

Links

Clark Kimberling, Table of n, a(n) for n = 1..200

Formula

a(n) = A226183(n) - n. - Michel Marcus, Sep 09 2021

Example

a(3) = 19 because 1/4 + 1/5 + ... + 1/(3+18) < 1 + 1/2 + 1/3 < 1/4 + 1/5 + ... + 1/(3+19).

Mathematica

z = 55; f[n_] := 1/n; p[n_] := p[n] = Sum[f[k], {k, 1, n}]; Do[s = 0; a[n] = NestWhile[# + 1 &, 1, ! (s += f[#]) >= 2 p[n] &], {n, 1, z}]; m = Map[a, Range[z]]  (* A226183 *)
m1 = Table[m[[n]] - n, {n, 1, z}] (* A226184 *)

Crossrefs

Cf. A226183, A289183.

Sequence in context: A294401 A194139 A194115 * A389614 A066506 A058331

Adjacent sequences: A226181 A226182 A226183 * A226185 A226186 A226187

Keyword

nonn

Author

Clark Kimberling, May 30 2013

Status

approved