login
A226188
Least positive integer k such that 1 + 1/2 + ... + 1/k > 2n/3.
1
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]
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
Sequence in context: A210003 A209888 A210021 * A239556 A152718 A347776
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