OFFSET
1,2
COMMENTS
Conjecture: a(n+1)/a(n) converges to 1.8552...
Conjecture confirmed: using series expansion of HarmonicNumber(k) one gets a(n+1)/a(n) -> exp(1/tau) = 1.855276958... [Jean-François Alcover, Jun 04 2013]
EXAMPLE
a(4) = 7 because 1 + 1/2 + ... + 1/6 < 4*tau < 1 + 1/2 + ... + 1/7.
MATHEMATICA
nn = 24; g = 1/GoldenRatio; f[n_] := 1/n; a[1] = 1; Do[s = 0; a[n] = NestWhile[# + 1 &, 1, ! (s += f[#]) > n*g &], {n, 1, nn}]; Map[a, Range[nn]]
CROSSREFS
KEYWORD
nonn
AUTHOR
Clark Kimberling, May 29 2013
EXTENSIONS
More terms from Jean-François Alcover, Jun 04 2013
STATUS
approved