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A092753
a(n) = smallest m >= 1 such that Sum_{k=1..m} log(k)/k >= n.
0
1, 4, 8, 12, 17, 24, 33, 43, 56, 71, 89, 111, 136, 166, 201, 242, 290, 345, 408, 481, 565, 660, 768, 892, 1031, 1190, 1368, 1569, 1796, 2049, 2334, 2652, 3008, 3405, 3847, 4339, 4885, 5491, 6162, 6905, 7726, 8634, 9634, 10737, 11951, 13287, 14754, 16364
OFFSET
0,2
COMMENTS
Sum (-1)^k log(k) / k is a conditionally convergent sequence that converges to gamma log(2) - (log 2)^2 / 2. But the sum of the absolute values diverges.
EXAMPLE
The sum of the first 4 terms is 1.059351276782648539882313867..., just >= 1, so a(1) = 4.
MATHEMATICA
f[n_] := Block[{s = 0, k = 1}, While[s = N[s + Log[k]/k, 128]; s < n, k++ ]; k]; Table[ f[n], {n, 0, 47}] (* Robert G. Wilson v, Apr 15 2004 *)
CROSSREFS
Cf. A002387.
Sequence in context: A340266 A194274 A098573 * A376852 A276338 A079774
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Apr 13 2004
EXTENSIONS
More terms from Robert G. Wilson v and Don Reble, Apr 15 2004
STATUS
approved