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A196519 Decimal expansion of the number x satisfying x*e^x=6.

%I A196519 #13 May 14 2019 23:41:36
%S A196519 1,4,3,2,4,0,4,7,7,5,8,9,8,3,0,0,3,1,1,2,3,4,0,7,8,0,0,7,2,1,2,0,5,8,
%T A196519 6,9,4,7,8,6,4,3,4,6,0,8,8,0,4,3,0,2,0,2,5,6,5,5,9,4,8,4,9,6,3,4,3,3,
%U A196519 9,9,5,9,3,2,5,9,8,3,1,1,1,6,8,5,7,6,3,8,4,2,2,2,9,9,4,4,5,6,5,1
%N A196519 Decimal expansion of the number x satisfying x*e^x=6.
%H A196519 G. C. Greubel, <a href="/A196519/b196519.txt">Table of n, a(n) for n = 1..5000</a>
%H A196519 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>
%e A196519 1.43240477589830031123407800721205869478643460...
%t A196519 Plot[{E^x, 1/x, 2/x, 3/x, 4/x}, {x, 0, 2}]
%t A196519 t = x /. FindRoot[E^x == 1/x, {x, 0.5, 1}, WorkingPrecision -> 100]
%t A196519 RealDigits[t]  (* A030175 *)
%t A196519 t = x /. FindRoot[E^x == 2/x, {x, 0.5, 1}, WorkingPrecision -> 100]
%t A196519 RealDigits[t]  (* A196515 *)
%t A196519 t = x /. FindRoot[E^x == 3/x, {x, 0.5, 2}, WorkingPrecision -> 100]
%t A196519 RealDigits[t]  (* A196516 *)
%t A196519 t = x /. FindRoot[E^x == 4/x, {x, 0.5, 2}, WorkingPrecision -> 100]
%t A196519 RealDigits[t]  (* A196517 *)
%t A196519 t = x /. FindRoot[E^x == 5/x, {x, 0.5, 2}, WorkingPrecision -> 100]
%t A196519 RealDigits[t]  (* A196518 *)
%t A196519 t = x /. FindRoot[E^x == 6/x, {x, 0.5, 2}, WorkingPrecision -> 100]
%t A196519 RealDigits[t]  (* A196519 *)
%t A196519 RealDigits[LambertW[6], 10, 50][[1]] (* _G. C. Greubel_, Nov 16 2017 *)
%o A196519 (PARI) lambertw(6) \\ _G. C. Greubel_, Nov 16 2017
%K A196519 nonn,cons
%O A196519 1,2
%A A196519 _Clark Kimberling_, Oct 03 2011
%E A196519 Terms a(95) onward corrected by _G. C. Greubel_, Nov 16 2017