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A096580 a(n) = smallest m >= 2 such that Sum_{k=2..m} 1/(k*log(k)) >= n. 8
2, 3, 28, 8718, 51426757439 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,1
COMMENTS
The sum diverges (see link), so a(n) is well-defined.
LINKS
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(n-k)), 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 * A371024 A351693 A324941
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

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Last modified June 25 11:48 EDT 2024. Contains 373701 sequences. (Running on oeis4.)