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A202392 Decimal expansion of the number x satisfying 3x=exp(-x).

%I A202392 #18 Feb 07 2025 16:44:07
%S A202392 2,5,7,6,2,7,6,5,3,0,4,9,7,3,6,7,0,4,2,8,2,9,1,6,2,0,1,6,2,6,0,9,7,7,
%T A202392 9,0,9,0,9,6,9,2,6,4,7,5,0,3,2,0,4,4,9,1,5,3,3,9,5,1,1,4,4,0,6,6,3,1,
%U A202392 9,1,2,9,2,7,5,2,0,4,3,7,2,4,5,9,6,3,9,8,8,7,9,3,4,1,0,0,2,5,0
%N A202392 Decimal expansion of the number x satisfying 3x=exp(-x).
%C A202392 See A202322 for a guide to related sequences. The Mathematica program includes a graph.
%H A202392 G. C. Greubel, <a href="/A202392/b202392.txt">Table of n, a(n) for n = 0..5000</a>
%H A202392 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>
%e A202392 x=0.257627653049736704282916201626097790909692...
%t A202392 u = 3; v = 0;
%t A202392 f[x_] := u*x + v; g[x_] := E^-x
%t A202392 Plot[{f[x], g[x]}, {x, 0, 1}, {AxesOrigin -> {0, 0}}]
%t A202392 r = x /. FindRoot[f[x] == g[x], {x, .25, .26}, WorkingPrecision -> 110]
%t A202392 RealDigits[r]  (* A202392 *)
%t A202392 (* other program *)
%t A202392 RealDigits[ ProductLog[1/3], 10, 99] // First (* _Jean-François Alcover_, Feb 14 2013 *)
%o A202392 (PARI) lambertw(1/3) \\ _G. C. Greubel_, Jun 10 2017
%Y A202392 Cf. A202322.
%K A202392 nonn,cons
%O A202392 0,1
%A A202392 _Clark Kimberling_, Dec 18 2011