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A366565
Decimal expansion of the smaller real solution to x*2^(1/x) = e.
0
3, 2, 7, 5, 6, 2, 4, 1, 3, 9, 7, 7, 5, 1, 6, 9, 4, 0, 0, 9, 2, 8, 2, 0, 8, 1, 2, 5, 9, 9, 1, 2, 2, 0, 4, 4, 3, 3, 9, 6, 4, 4, 6, 9, 6, 6, 5, 4, 2, 2, 7, 4, 2, 0, 4, 2, 9, 6, 9, 6, 9, 5, 4, 9, 6, 3, 4, 7, 6, 6, 3, 1, 4, 2, 2, 3, 3, 8, 7, 4, 9, 7, 5, 4, 6, 7, 9, 4, 2
OFFSET
0,1
COMMENTS
This is the constant alpha occurring in the asymptotic analysis of random walks on the hypercube (Lemma 3, page 7, attributed to Bjorn Poonen), in Diaconis, Graham, and Morrison (1988). See link for more information.
LINKS
Persi Diaconis, R. L. Graham, and J. A. Morrison, Asymptotic Analysis of a Random Walk on a Hypercube with Many Dimensions, Technical Report EFS NFS 307, Department of Statistics, Stanford University, December 1988.
Persi Diaconis, R. L. Graham, and J. A. Morrison, Asymptotic analysis of a random walk on a hypercube with many dimensions, Random Structures & Algorithms, Volume 1, Issue 1, Pages 51-72, Spring 1990.
Gordon Slade, Self-avoiding walk on the hypercube, Random Structures & Algorithms, Volume 62, Issue 3, May 2023, Pages 689-736.
FORMULA
Equals -log(2)/LambertW(-1, -log(2)/exp(1)). - Vaclav Kotesovec, Nov 03 2023
EXAMPLE
0.32756241397751694009282081259912204433964469665422742...
MATHEMATICA
RealDigits[-Log[2]/ProductLog[-1, -Log[2]/E], 10, 120][[1]] (* Vaclav Kotesovec, Nov 03 2023 *)
PROG
(PARI) solve (x = 0.3, 0.35, x*2^(1/x)-exp(1))
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Hugo Pfoertner, Oct 23 2023
STATUS
approved