A366565 Decimal expansion of the smaller real solution to x*2^(1/x) = e.

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

Author

Hugo Pfoertner, Oct 23 2023

Keywords

• nonn
• cons

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.

Examples

			0.32756241397751694009282081259912204433964469665422742...
		

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.

Crossrefs

Cf. A001113, A003149, A324495.

Programs

Mathematica

RealDigits[-Log[2]/ProductLog[-1, -Log[2]/E], 10, 120][[1]] (* Vaclav Kotesovec, Nov 03 2023 *)

PARI

solve (x = 0.3, 0.35, x*2^(1/x)-exp(1))

Formula

Equals -log(2)/LambertW(-1, -log(2)/exp(1)). - Vaclav Kotesovec, Nov 03 2023