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Decimal expansion of x^x^x^x^... when x = 11/10.
1

%I #16 Oct 21 2018 16:16:06

%S 1,1,1,1,7,8,2,0,1,1,0,4,1,8,4,3,3,2,2,2,4,4,8,6,2,6,7,5,3,5,0,5,3,3,

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

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

%N Decimal expansion of x^x^x^x^... when x = 11/10.

%C Suggested by a remark in the Applegate et al. paper.

%D David Applegate, Marc LeBrun and N. J. A. Sloane, Descending Dungeons and Iterated Base-Changing, in "The Mathematics of Preference, Choice and Order: Essays in Honor of Peter Fishburn", edited by Steven Brams, William V. Gehrlein and Fred S. Roberts, Springer, 2009, pp. 393-402.

%H Alois P. Heinz, <a href="/A126625/b126625.txt">Table of n, a(n) for n = 1..10000</a>

%H David Applegate, Marc LeBrun and N. J. A. Sloane, <a href="https://arxiv.org/abs/math/0611293">Descending Dungeons and Iterated Base-Changing</a>, arXiv:math/0611293 [math.NT], 2006-2007.

%H David Applegate, Marc LeBrun and N. J. A. Sloane, <a href="https://www.jstor.org/stable/40391135">Descending Dungeons, Problem 11286</a>, Amer. Math. Monthly, 116 (2009) 466-467.

%e 1.1117820110418433222448626753505335401387930...

%p x:= LambertW(log(10/11))/log(10/11)/10:

%p s:= convert(evalf(x, 140), string):

%p seq(parse(s[n+1]), n=1..120); # _Alois P. Heinz_, Nov 08 2015

%t RealDigits[-ProductLog[-Log[11/10]]/(10*Log[11/10]), 10, 105][[1]] (* _Jean-François Alcover_, Feb 18 2016 *)

%K nonn,cons

%O 1,5

%A _N. J. A. Sloane_, Feb 10 2007