cp's OEIS Frontend

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

%I A366565 #23 Nov 03 2023 11:18:04
%S A366565 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,
%T A366565 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,
%U A366565 6,6,3,1,4,2,2,3,3,8,7,4,9,7,5,4,6,7,9,4,2
%N A366565 Decimal expansion of the smaller real solution to x*2^(1/x) = e.
%C A366565 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.
%H A366565 Persi Diaconis, R. L. Graham, and J. A. Morrison, <a href="http://web.archive.org/web/20190917054306/https://statistics.stanford.edu/research/asymptotic-analysis-random-walk-hypercube-many-dimensions">Asymptotic Analysis of a Random Walk on a Hypercube with Many Dimensions</a>, Technical Report EFS NFS 307, Department of Statistics, Stanford University, December 1988.
%H A366565 Persi Diaconis, R. L. Graham, and J. A. Morrison, <a href="https://doi.org/10.1002/rsa.3240010105">Asymptotic analysis of a random walk on a hypercube with many dimensions</a>, Random Structures & Algorithms, Volume 1, Issue 1, Pages 51-72, Spring 1990.
%H A366565 Gordon Slade, <a href="https://doi.org/10.1002/rsa.21117">Self-avoiding walk on the hypercube</a>, Random Structures & Algorithms, Volume 62, Issue 3, May 2023, Pages 689-736.
%F A366565 Equals -log(2)/LambertW(-1, -log(2)/exp(1)). - _Vaclav Kotesovec_, Nov 03 2023
%e A366565 0.32756241397751694009282081259912204433964469665422742...
%t A366565 RealDigits[-Log[2]/ProductLog[-1, -Log[2]/E], 10, 120][[1]] (* _Vaclav Kotesovec_, Nov 03 2023 *)
%o A366565 (PARI) solve (x = 0.3, 0.35, x*2^(1/x)-exp(1))
%Y A366565 Cf. A001113, A003149, A324495.
%K A366565 nonn,cons
%O A366565 0,1
%A A366565 _Hugo Pfoertner_, Oct 23 2023