

A096580


a(n) = smallest m >= 2 such that Sum_{k=2..m} 1/(k*log(k)) >= n.


8




OFFSET

0,1


COMMENTS

The sum diverges (see link), so a(n) is welldefined.


LINKS

Table of n, a(n) for n=0..4.
M. Goar, Olivier and Abel on series convergence: An episode from early 19th century analysis, Math. Mag., 72 (No. 5, 1999), 347355.


FORMULA

Since Integral 1/(x*log(x)) dx = log log x, a(n) is close to e^(e^n) (cf. A096232, A096404, A016066).
a(n) is roughly exp(exp(nk)), where k = 0.7946786454...  Charles R Greathouse IV, Jul 23 2007


EXAMPLE

For m = 27 the sum is 1.992912323604..., for m = 28 it is 2.0036302389..., so a(2) = 28.
For m = 8717 the sum is 2.999991290360..., for m = 8718 it is 3.0000039326..., so a(3) = 8718.


MATHEMATICA

n = 0; m = 2; sum = 1/(m*Log[m]); lst = {};
While[n <= 3,
While[ sum < n, m++; sum += 1/(m*Log[m])];
AppendTo[lst, m]; n++]; lst (* Robert Price, Apr 09 2019 *)


CROSSREFS

Cf. A016088.
Sequence in context: A319146 A206591 A003017 * A351693 A324941 A028868
Adjacent sequences: A096577 A096578 A096579 * A096581 A096582 A096583


KEYWORD

nonn,more,hard


AUTHOR

N. J. A. Sloane, Aug 13 2004


EXTENSIONS

a(3) from Robert G. Wilson v, Aug 17 2004
a(4) from Charles R Greathouse IV, Jul 23 2007


STATUS

approved



