A226188 Least positive integer k such that 1 + 1/2 + ... + 1/k > 2n/3.

1, 2, 4, 8, 16, 31, 60, 116, 227, 441, 859, 1674, 3260, 6349, 12367, 24088, 46916, 91380, 177984, 346666, 675214, 1315136, 2561536, 4989191, 9717617, 18927334, 36865412

Offset

1,2

Comments

Conjecture: a(n+1)/a(n) converges to 1.94...

Conjecture confirmed: series expansion of HarmonicNumber(k) gives a(n+1)/a(n) -> exp(2/3) = 1.947734... [Jean-François Alcover, Jun 05 2013]

Links

Table of n, a(n) for n=1..27.

Example

a(8) = 116 because 1 + 1/2 + ... + 1/115 < 16/3 < 1 + 1/2 + ... + 1/116.

Mathematica

z = 18; f[n_] := 1/n; Do[s = 0; a[n] = NestWhile[# + 1 &, 1, ! (s += f[#]) >= 2n/3 &], {n, 1, z}]; m = Map[a, Range[z]]

Crossrefs

Cf. A226186, A226187.

Sequence in context: A210003 A209888 A210021 * A239556 A152718 A347776

Adjacent sequences: A226185 A226186 A226187 * A226189 A226190 A226191

Keyword

nonn,more

Author

Clark Kimberling, May 30 2013

Extensions

More terms from Jean-François Alcover, Jun 05 2013

Deleted obsolete b-file. - N. J. A. Sloane, Jan 04 2019

Status

approved