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%I #18 May 14 2019 23:48:01
%S 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 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 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 Decimal expansion of the number x satisfying 2*x + 2 = exp(-x), negated.
%C See A202322 for a guide to related sequences. The Mathematica program includes a graph.
%H G. C. Greubel, <a href="/A202353/b202353.txt">Table of n, a(n) for n = 0..5000</a>
%F Equals W(e/2) - 1, where W(x) is the Lambert W-function. - _G. C. Greubel_, Jun 09 2017
%e x = -0.3149230578454060539717505194623698115859...
%t u = 2; v = 2;
%t f[x_] := u*x + v; g[x_] := E^-x
%t Plot[{f[x], g[x]}, {x, -1, 1}, {AxesOrigin -> {0, 0}}]
%t r = x /. FindRoot[f[x] == g[x], {x, -.4, -.3}, WorkingPrecision -> 110]
%t RealDigits[r] (* A202353 *)
%t (* other program *)
%t RealDigits[ ProductLog[E/2] - 1, 10, 99] // First (* _Jean-François Alcover_, Feb 14 2013 *)
%o (PARI) lambertw(exp(1)/2) - 1 \\ _G. C. Greubel_, Jun 09 2017
%Y Cf. A202322.
%K nonn,cons
%O 0,1
%A _Clark Kimberling_, Dec 18 2011
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