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A202353 Decimal expansion of the number x satisfying 2*x + 2 = exp(-x), negated.

%I A202353 #21 Feb 07 2025 16:44:07
%S A202353 3,1,4,9,2,3,0,5,7,8,4,5,4,0,6,0,5,3,9,7,1,7,5,0,5,1,9,4,6,2,3,6,9,8,
%T A202353 1,1,5,8,5,9,4,4,2,8,4,3,1,9,1,7,9,4,6,6,4,5,9,0,1,9,8,4,5,0,1,2,4,9,
%U A202353 6,1,2,1,4,8,8,8,1,1,8,5,2,1,8,8,0,3,4,4,4,4,4,8,2,0,8,0,0,7,6
%N A202353 Decimal expansion of the number x satisfying 2*x + 2 = exp(-x), negated.
%C A202353 See A202322 for a guide to related sequences. The Mathematica program includes a graph.
%H A202353 G. C. Greubel, <a href="/A202353/b202353.txt">Table of n, a(n) for n = 0..5000</a>
%H A202353 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>
%F A202353 Equals W(e/2) - 1, where W(x) is the Lambert W-function. - _G. C. Greubel_, Jun 09 2017
%e A202353 x = -0.3149230578454060539717505194623698115859...
%t A202353 u = 2; v = 2;
%t A202353 f[x_] := u*x + v; g[x_] := E^-x
%t A202353 Plot[{f[x], g[x]}, {x, -1, 1}, {AxesOrigin -> {0, 0}}]
%t A202353 r = x /. FindRoot[f[x] == g[x], {x, -.4, -.3}, WorkingPrecision -> 110]
%t A202353 RealDigits[r] (* A202353 *)
%t A202353 (* other program *)
%t A202353 RealDigits[ ProductLog[E/2] - 1, 10, 99] // First (* _Jean-François Alcover_, Feb 14 2013 *)
%o A202353 (PARI) lambertw(exp(1)/2) - 1 \\ _G. C. Greubel_, Jun 09 2017
%Y A202353 Cf. A202322.
%K A202353 nonn,cons
%O A202353 0,1
%A A202353 _Clark Kimberling_, Dec 18 2011