cp's OEIS Frontend

A363229 Decimal expansion of e^(-2*LambertW(-log(2)/4)).

%I A363229 #34 May 23 2023 08:16:27
%S A363229 1,5,3,6,6,7,6,9,0,7,8,0,1,7,5,8,3,3,4,6,1,2,4,7,5,0,3,0,9,0,5,0,3,7,
%T A363229 8,3,1,7,9,8,3,6,1,0,5,6,6,0,9,0,3,8,8,1,2,0,7,6,8,3,4,8,5,6,5,8,9,1,
%U A363229 9,8,5,9,4,4,7,8,4,7,5,5,7,5,8,7,1,7,1,0,5,5,7,1,4,6,9,8,2,3,7
%N A363229 Decimal expansion of e^(-2*LambertW(-log(2)/4)).
%C A363229 The least real solution of x^2 = 2^sqrt(x). This equation has two real solutions the other is 256.
%C A363229 Let x be this constant, and c = 2*log(x)/log(2); then c^4 = 2^c.
%C A363229 Let x be this constant, and c = 1/sqrt(x); then c^c = 1/2^(1/4).
%F A363229 Equals e^(-2*Sum_{k>=1} ((-k)^(-1+k)*(-log(2)/4)^k/k!)).
%F A363229 Equals e^(t*log(2)/2) where t = (2^(1/4))^(2^(1/4))^(2^(1/4))^(2^(1/4))^... is the infinite power tower over 2^(1/4).
%F A363229 Equals 16*LambertW(-log(2)/4)^2 / log(2)^2. - _Vaclav Kotesovec_, May 22 2023
%e A363229 1.5366769...
%t A363229 RealDigits[E^(-2 ProductLog[-Log[2]/4]),10,100][[1]]
%o A363229 (PARI)
%o A363229 \p 200
%o A363229 exp(-2*lambertw(-log(2)/4))
%o A363229 (Python)
%o A363229 import math; from sympy import LambertW
%o A363229 print([i for i in str("%.30f" % math.exp(-2*LambertW(-math.log(2)/4)))])
%o A363229 # _Javier Rivera Romeu_, May 22 2023
%Y A363229 Cf. A073084, A104750.
%K A363229 nonn,cons
%O A363229 1,2
%A A363229 _Thomas Scheuerle_, May 22 2023