A092753 - OEIS

A092753

a(n) = smallest m >= 1 such that Sum_{k=1..m} log(k)/k >= n.

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

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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.

LINKS

Table of n, a(n) for n=0..47.

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

Adjacent sequences: A092750 A092751 A092752 * A092754 A092755 A092756

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