|
| |
|
|
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 reference), so a(n) is well-defined.
|
|
|
REFERENCES
| M. Goar, Olivier and Abel on series convergence: An episode from early 19th century analysis, Math. Mag., 72 (No. 5, 1999), 347-355.
|
|
|
LINKS
| Charles R Greathouse IV, Home Page [in lieu of email address]
|
|
|
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.
|
|
|
CROSSREFS
| Cf. A016088.
Sequence in context: A126266 A206591 A003017 * A028868 A081332 A106868
Adjacent sequences: A096577 A096578 A096579 * A096581 A096582 A096583
|
|
|
KEYWORD
| nonn,more
|
|
|
AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Aug 13 2004
|
|
|
EXTENSIONS
| 8718 from Robert G. Wilson v, Aug 17 2004
a(4) from Charles R Greathouse IV, Jul 23 2007
|
| |
|
|
