A226187 - OEIS

A226187

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

1, 1, 1, 2, 3, 4, 6, 8, 11, 16, 22, 31, 43, 60, 83, 116, 162, 227, 316, 441, 616, 859, 1199, 1674, 2336, 3260, 4550, 6349, 8861, 12367, 17259, 24088, 33617, 46916, 65477, 91380, 127531, 177984, 248397, 346666, 483812, 675214, 942336, 1315136, 1835421, 2561536, 3574912, 4989191, 6962977, 9717617

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OFFSET

1,4

COMMENTS

Conjecture: a(n+1)/a(n) converges to 1.39...

This constant is probably exp(1/3) = 1.395612425086089528628..., see A004080. - Ralf Stephan, Jun 03 2013

LINKS

Table of n, a(n) for n=1..50.

EXAMPLE

a(10) = 16 because 1 + 1/2 + ... + 1/15 < 10/3 < 1 + 1/2 + ... + 1/16.

MATHEMATICA

z = 32; f[n_] := 1/n; Do[s = 0; a[n] = NestWhile[# + 1 &, 1, ! (s += f[#]) >= n/3 &], {n, 1, z}]; m = Map[a, Range[z]]