A141251 Decimal expansion of the number c satisfying c*log(c)=1+c.

3, 5, 9, 1, 1, 2, 1, 4, 7, 6, 6, 6, 8, 6, 2, 2, 1, 3, 6, 6, 4, 9, 2, 2, 2, 9, 2, 5, 7, 4, 1, 6, 3, 4, 8, 4, 2, 1, 0, 3, 0, 7, 5, 4, 0, 1, 5, 9, 2, 7, 8, 6, 9, 1, 9, 0, 4, 5, 2, 9, 8, 7, 3, 1, 9, 9, 2, 2, 6, 5, 4, 9, 8, 4, 4, 0, 3, 1, 6, 3, 7, 6, 6, 0, 2, 3, 6, 4, 1, 7, 7, 4, 6, 5, 2, 4, 5, 7, 1

Offset: 1

Author

David Applegate and N. J. A. Sloane, Sep 04 2008

Keywords

• nonn
• cons

Comments

The iteration on c = c*log(c)- 1 does not converge from above or below. However, iteration on c = exp(1+1/c) converges quickly from above and below, including negative values. - Richard R. Forberg, Dec 28 2013

c is the solution to the equation 2 = Integral_{t=1...c} log(t) dt. - Colin Linzer, Nov 12 2024

Examples

			3.59112147666862213664922292574163484210307540159278691904529873...
		

Links

• G. C. Greubel, Table of n, a(n) for n = 1..5000
• Luigi Addario-Berry, Nicolas Broutin and Gabor Lugosi, The longest minimum-weight path in a complete graph, arXiv:0809.0275 [math.CO], 2008-2009.
• Steven R. Finch and Li-Yan Zhu, Searching for a Shoreline, arXiv:math/0501123 [math.OC], 2005, p. 10.
• Michel Goemans and Jon Kleinberg, An improved approximation ratio for the minimum latency problem, Proc. 7th ACM-SIAM Symposium on Discrete Algorithms, 1996, pp. 152-158.
• Henryk Iwaniec, Rosser's sieve, Acta Arithmetica 36:2 (1980), pp. 171-202.
• Index entries for transcendental numbers

Crossrefs

Cf. A141252.

Programs

Mathematica

RealDigits[ 1 / ProductLog[ 1/E ], 10, 99] // First (* Jean-François Alcover, Mar 07 2013 *)

PARI

solve(x=3,4,x*log(x)-x-1) \\ Charles R Greathouse IV, Feb 22 2016

PARI

exp(lambertw(exp(-1))+1) \\ Charles R Greathouse IV, Feb 22 2016

Formula

Equals exp(LambertW(1/e)+1).

Equals 1/A202357. - Hugo Pfoertner, Nov 12 2024