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A141251 Decimal expansion of the number c satisfying c*log(c)=1+c. 6

%I

%S 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,

%T 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,

%U 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

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

%C 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

%H G. C. Greubel, <a href="/A141251/b141251.txt">Table of n, a(n) for n = 1..5000</a>

%H Luigi Addario-Berry, Nicolas Broutin and Gabor Lugosi, <a href="http://arxiv.org/abs/0809.0275">The longest minimum-weight path in a complete graph</a>, arXiv:0809.0275 [math.CO], 2008-2009.

%H Steven R. Finch and Li-Yan Zhu, <a href="http://arxiv.org/abs/math/0501123">Searching for a Shoreline</a>, arXiv:math/0501123 [math.OC], 2005, p. 10.

%H Michel Goemans and Jon Kleinberg, <a href="http://dx.doi.org/10.1007/BF01585867">An improved approximation ratio for the minimum latency problem</a>, Proc. 7th ACM-SIAM Symposium on Discrete Algorithms, 1996, pp. 152-158.

%H Henryk Iwaniec, <a href="http://matwbn.icm.edu.pl/ksiazki/aa/aa36/aa36210.pdf">Rosser's sieve</a>, Acta Arithmetica 36:2 (1980), pp. 171-202.

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

%e 3.59112147666862213664922292574163484210307540159278691904529873...

%t RealDigits[ 1 / ProductLog[ 1/E ], 10, 99] // First (* _Jean-Fran├žois Alcover_, Mar 07 2013 *)

%o (PARI) solve(x=3,4,x*log(x)-x-1) \\ _Charles R Greathouse IV_, Feb 22 2016

%o (PARI) exp(lambertw(exp(-1))+1) \\ _Charles R Greathouse IV_, Feb 22 2016

%Y Cf. A141252.

%K nonn,cons

%O 1,1

%A _David Applegate_ and _N. J. A. Sloane_, Sep 04 2008

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Last modified June 13 09:54 EDT 2021. Contains 344981 sequences. (Running on oeis4.)