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A202356 Decimal expansion of the number x satisfying 2x=exp(-x).

%I A202356 #15 Feb 07 2025 16:44:07
%S A202356 3,5,1,7,3,3,7,1,1,2,4,9,1,9,5,8,2,6,0,2,4,9,0,9,3,0,0,9,2,9,9,5,1,0,
%T A202356 6,5,1,7,1,4,6,4,2,1,5,5,1,7,1,1,1,8,0,4,0,4,6,6,4,3,8,4,6,1,0,9,9,6,
%U A202356 0,6,1,0,7,2,0,3,3,8,7,1,0,8,9,6,8,3,2,3,0,3,8,3,2,1,9,1,5,6,9
%N A202356 Decimal expansion of the number x satisfying 2x=exp(-x).
%C A202356 See A202322 for a guide to related sequences. The Mathematica program includes a graph.
%H A202356 G. C. Greubel, <a href="/A202356/b202356.txt">Table of n, a(n) for n = 0..5000</a>
%H A202356 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>
%e A202356 x=0.35173371124919582602490930092995106517146...
%t A202356 u = 2; v = 0;
%t A202356 f[x_] := u*x + v; g[x_] := E^-x
%t A202356 Plot[{f[x], g[x]}, {x, 0, 2}, {AxesOrigin -> {0, 0}}]
%t A202356 r = x /. FindRoot[f[x] == g[x], {x, .35, .36}, WorkingPrecision -> 110]
%t A202356 RealDigits[r] (* A202356 *)
%t A202356 RealDigits[ ProductLog[1/2], 10, 99] // First (* _Jean-François Alcover_, Feb 14 2013 *)
%o A202356 (PARI) lambertw(1/2) \\ _G. C. Greubel_, Jun 10 2017
%Y A202356 Cf. A202322.
%K A202356 nonn,cons
%O A202356 0,1
%A A202356 _Clark Kimberling_, Dec 18 2011