Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the 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