A202538 - OEIS

%I #10 May 15 2019 00:22:32

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

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

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

%N Decimal expansion of the number x satisfying e^x-e^(-3x)=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 x=0.32228461597103006003623548628913923545544311...

%t u = 1; v = 3;

%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, .3, .4}, WorkingPrecision -> 110]

%t RealDigits[r]  (* A202538 *)

%t RealDigits[ Log[ Root[#^4 - #^3 - 1&, 2]], 10, 99] // First (* _Jean-François Alcover_, Feb 27 2013 *)

%o (PARI) log(polrootsreal(x^4-x^3-1)[2]) \\ _Charles R Greathouse IV_, May 15 2019

%Y Cf. A202537.

%K nonn,cons

%O 0,1

%A _Clark Kimberling_, Dec 21 2011