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

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]]

Prog

(PARI) a(n)=local(s, k); s=0; k=1; while(s<=n/3, s=s+1/k; k++); k-1

Crossrefs

Cf. A226186, A226188, A002387, A004080.

Sequence in context: A321567 A066806 A271486 * A294922 A317669 A208887

Adjacent sequences: A226184 A226185 A226186 * A226188 A226189 A226190

Keyword

nonn

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