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%I #4 Jun 04 2013 03:27:41
%S 1,1,2,2,3,3,4,4,5,6,6,7,7,8,8,9,10,10,11,11,12,12,13,13,14,15,15,16,
%T 16,17,17,18,19,19,20,20,21,21,22,22,23,24,24,25,25,26,26,27,28,28,29,
%U 29,30,30,31,31,32,33,33,34,34,35,35,36,36,37,38,38,39,39,40,40,41,42,42,43,43,44,44,45
%N Least positive integer k such that 1 + 1/2 + ... + 1/k >= log(n).
%H Clark Kimberling, <a href="/A226190/b226190.txt">Table of n, a(n) for n = 1..1000</a>
%e a(9) = 5 because 1 + 1/2 + 1/3 + 1/4 < log(9) < 1 + 1/2 + 1/3 + 1/4 + 1/5.
%t z = 80; f[n_] := 1/n; Do[s = 0; a[n] = NestWhile[# + 1 &, 1, ! (s += f[#]) > Log[n] &], {n, 1, z}]; m = Map[a, Range[z]]
%Y Cf. A226183, A226189, A004081.
%K nonn
%O 1,3
%A _Clark Kimberling_, May 30 2013
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