A196517 - OEIS

%I #13 May 14 2019 23:41:16

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

%H G. C. Greubel, <a href="/A196517/b196517.txt">Table of n, a(n) for n = 1..5000</a>

%H <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>

%e 1.2021678731970429392120741654951534475015125218296259...

%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[4], 10, 50][[1]] (* _G. C. Greubel_, Nov 16 2017 *)

%o (PARI) lambertw(4) \\ _G. C. Greubel_, Nov 16 2017

%K nonn,cons

%O 1,2

%A _Clark Kimberling_, Oct 03 2011