%I #11 May 14 2019 23:54:54

%S 1,9,9,4,6,0,5,7,8,2,4,3,0,0,5,3,5,1,4,8,8,5,7,7,7,1,8,3,8,4,9,4,9,1,

%T 7,8,3,9,2,7,7,6,9,2,6,2,0,8,1,2,4,9,2,4,0,1,5,3,6,4,5,4,7,1,6,8,0,8,

%U 6,6,4,3,9,3,8,4,3,2,8,5,4,8,7,9,2,7,9,9,8,0,3,6,1,6,3,6,4,6,4

%N Decimal expansion of the number x satisfying e^(3x)-e^(-x)=1.

%C See A202537 for a guide to related sequences. The Mathematica program includes a graph.

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

%e 0.19946057824300535148857771838494917839277692...

%t u = 3; v = 1;

%t f[x_] := E^(u*x) - E^(-v*x); g[x_] := 1

%t Plot[{f[x], g[x]}, {x, -2, 2}, {AxesOrigin -> {0, 0}}]

%t r = x /. FindRoot[f[x] == g[x], {x, .1, .2}, WorkingPrecision -> 110]

%t RealDigits[r] (* A202540 *)

%t RealDigits[ Log[ Root[#^4 - # - 1&, 2]], 10, 99] // First (* _Jean-François Alcover_, Feb 27 2013 *)

%o (PARI) log(polrootsreal(x^4-x-1)[2]) \\ _Charles R Greathouse IV_, May 14 2019

%Y Cf. A202537.

%K nonn,cons

%O 0,2

%A _Clark Kimberling_, Dec 21 2011