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%I #13 May 14 2019 23:41:25
%S 1,3,2,6,7,2,4,6,6,5,2,4,2,2,0,0,2,2,3,6,3,5,0,9,9,2,9,7,7,5,8,0,7,9,
%T 6,6,0,1,2,8,7,9,3,5,5,4,6,3,8,0,4,7,4,7,9,7,8,9,2,9,0,3,9,3,0,2,5,3,
%U 4,2,6,7,9,9,2,0,5,3,6,2,2,6,7,7,4,4,6,9,9,1,6,6,0,8,4,2,6,7,8,9
%N Decimal expansion of the number x satisfying x*e^x=5.
%H G. C. Greubel, <a href="/A196518/b196518.txt">Table of n, a(n) for n = 1..5000</a>
%H <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>
%e 1.32672466524220022363509929775807966012...
%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[5], 10, 50][[1]] (* _G. C. Greubel_, Nov 16 2017 *)
%o (PARI) lambertw(5) \\ _G. C. Greubel_, Nov 16 2017
%K nonn,cons
%O 1,2
%A _Clark Kimberling_, Oct 03 2011
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