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A196517 Decimal expansion of the number x satisfying x*e^x=4.

%I A196517 #13 May 14 2019 23:41:16
%S A196517 1,2,0,2,1,6,7,8,7,3,1,9,7,0,4,2,9,3,9,2,1,2,0,7,4,1,6,5,4,9,5,1,5,3,
%T A196517 4,4,7,5,0,1,5,1,2,5,2,1,8,2,9,6,2,5,9,8,1,7,3,9,2,0,3,5,9,0,7,0,0,6,
%U A196517 3,4,1,3,2,9,8,1,7,7,2,6,7,7,2,2,7,8,2,6,1,0,4,9,7,6,5,6,8,3,7,7
%N A196517 Decimal expansion of the number x satisfying x*e^x=4.
%H A196517 G. C. Greubel, <a href="/A196517/b196517.txt">Table of n, a(n) for n = 1..5000</a>
%H A196517 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>
%e A196517 1.2021678731970429392120741654951534475015125218296259...
%t A196517 Plot[{E^x, 1/x, 2/x, 3/x, 4/x}, {x, 0, 2}]
%t A196517 t = x /. FindRoot[E^x == 1/x, {x, 0.5, 1}, WorkingPrecision -> 100]
%t A196517 RealDigits[t]  (* A030175 *)
%t A196517 t = x /. FindRoot[E^x == 2/x, {x, 0.5, 1}, WorkingPrecision -> 100]
%t A196517 RealDigits[t]  (* A196515 *)
%t A196517 t = x /. FindRoot[E^x == 3/x, {x, 0.5, 2}, WorkingPrecision -> 100]
%t A196517 RealDigits[t]  (* A196516 *)
%t A196517 t = x /. FindRoot[E^x == 4/x, {x, 0.5, 2}, WorkingPrecision -> 100]
%t A196517 RealDigits[t]  (* A196517 *)
%t A196517 t = x /. FindRoot[E^x == 5/x, {x, 0.5, 2}, WorkingPrecision -> 100]
%t A196517 RealDigits[t]  (* A196518 *)
%t A196517 t = x /. FindRoot[E^x == 6/x, {x, 0.5, 2}, WorkingPrecision -> 100]
%t A196517 RealDigits[t]  (* A196519 *)
%t A196517 RealDigits[LambertW[4], 10, 50][[1]] (* _G. C. Greubel_, Nov 16 2017 *)
%o A196517 (PARI) lambertw(4) \\ _G. C. Greubel_, Nov 16 2017
%K A196517 nonn,cons
%O A196517 1,2
%A A196517 _Clark Kimberling_, Oct 03 2011