%I
%S 1,0,4,9,9,0,8,8,9,4,9,6,4,0,3,9,9,5,9,9,8,8,6,9,7,0,7,0,5,5,2,8,9,7,
%T 9,0,4,5,8,9,4,6,6,9,4,3,7,0,6,3,4,1,4,5,2,9,3,2,8,7,1,5,8,3,3,1,6,6,
%U 4,9,0,5,0,4,4,4,4,4,2,9,5,7,8,8,5,6,7,8,6,6,6,8,2,2,4,3,4,6,7,4
%N Decimal expansion of the number x satisfying x*e^x=3.
%H G. C. Greubel, <a href="/A196516/b196516.txt">Table of n, a(n) for n = 1..5000</a>
%H <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>
%e 1.049908894964039959988697070552897904589...
%t Plot[{E^x, 1/x, 2/x, 3/x, 4/x}, {x, 0, 2}]
%t t = x /. FindRoot[E^x == 1/x, {x, 0.5, 1}, WorkingPrecision > 100]
%t RealDigits[t] (* A030175 *)
%t t = x /. FindRoot[E^x == 2/x, {x, 0.5, 1}, WorkingPrecision > 100]
%t RealDigits[t] (* A196515 *)
%t t = x /. FindRoot[E^x == 3/x, {x, 0.5, 2}, WorkingPrecision > 100]
%t RealDigits[t] (* A196516 *)
%t t = x /. FindRoot[E^x == 4/x, {x, 0.5, 2}, WorkingPrecision > 100]
%t RealDigits[t] (* A196517 *)
%t t = x /. FindRoot[E^x == 5/x, {x, 0.5, 2}, WorkingPrecision > 100]
%t RealDigits[t] (* A196518 *)
%t t = x /. FindRoot[E^x == 6/x, {x, 0.5, 2}, WorkingPrecision > 100]
%t RealDigits[t] (* A196519 *)
%t RealDigits[LambertW[3], 10, 50][[1]] (* _G. C. Greubel, Nov 16 2017 *)
%o (PARI) lambertw(3) \\ _G. C. Greubel_, Nov 16 2017
%K nonn,cons
%O 1,3
%A _Clark Kimberling_, Oct 03 2011
