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%I #8 Feb 27 2013 05:26:37
%S 3,4,9,9,6,9,6,3,1,6,5,4,6,7,9,9,8,6,6,6,2,8,9,9,0,2,3,5,1,7,6,3,2,6,
%T 3,4,8,6,3,1,5,5,6,4,7,9,0,2,1,1,3,8,1,7,6,4,4,2,9,0,5,2,7,7,7,2,2,1,
%U 6,3,5,0,1,4,8,1,4,7,6,5,2,6,2,8,5,5,9,5,5,5,6,0,7,4,7,8,2,2,4
%N Decimal expansion of x satisfying x=e^(-3x).
%C See A202348 for a guide to related sequences. The Mathematica program includes a graph.
%e x=0.3499696316546799866628990235176326348631556...
%t u = -3; v = 0;
%t f[x_] := x; g[x_] := E^(u*x + v)
%t Plot[{f[x], g[x]}, {x, -1, 1}, {AxesOrigin -> {0, 0}}]
%t r = x /. FindRoot[f[x] == g[x], {x, .3, .4}, WorkingPrecision -> 110]
%t RealDigits[r] (* A202499 *)
%t RealDigits[ ProductLog[3]/3, 10, 99] // First (* _Jean-François Alcover_, Feb 27 2013 *)
%Y Cf. A202348.
%K nonn,cons
%O 0,1
%A _Clark Kimberling_, Dec 20 2011