A126625 - OEIS

A126625

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

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, 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, 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

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OFFSET

1,5

COMMENTS

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

REFERENCES

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.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..10000

David Applegate, Marc LeBrun and N. J. A. Sloane, Descending Dungeons and Iterated Base-Changing, arXiv:math/0611293 [math.NT], 2006-2007.

David Applegate, Marc LeBrun and N. J. A. Sloane, Descending Dungeons, Problem 11286, Amer. Math. Monthly, 116 (2009) 466-467.

EXAMPLE

1.1117820110418433222448626753505335401387930...

MAPLE

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

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

seq(parse(s[n+1]), n=1..120); # Alois P. Heinz, Nov 08 2015

MATHEMATICA

RealDigits[-ProductLog[-Log[11/10]]/(10*Log[11/10]), 10, 105][[1]] (* Jean-François Alcover, Feb 18 2016 *)