cp's OEIS Frontend

A202542 Decimal expansion of the number x satisfying e^(3x)-e^(-3x)=1.

%I A202542 #11 Feb 07 2025 16:44:07
%S A202542 1,6,0,4,0,3,9,4,1,6,8,6,5,3,4,4,8,2,4,9,9,2,5,2,9,7,1,1,4,1,4,5,6,1,
%T A202542 4,1,0,4,5,0,6,1,4,4,4,7,9,5,2,2,0,1,7,3,2,2,0,3,3,9,3,8,9,6,1,3,3,8,
%U A202542 7,9,5,5,8,6,9,4,0,7,2,5,8,1,3,7,3,3,6,4,7,6,3,7,4,2,4,1,1,5,8
%N A202542 Decimal expansion of the number x satisfying e^(3x)-e^(-3x)=1.
%C A202542 See A202537 for a guide to related sequences. The Mathematica program includes a graph.
%H A202542 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>
%e A202542 x=0.1604039416865344824992529711414561410450614447...
%t A202542 u = 3; v = 3;
%t A202542 f[x_] := E^(u*x) - E^(-v*x); g[x_] := 1
%t A202542 Plot[{f[x], g[x]}, {x, -1, 1}, {AxesOrigin -> {0, 0}}]
%t A202542 r = x /. FindRoot[f[x] == g[x], {x, .2, .3}, WorkingPrecision -> 110]
%t A202542 RealDigits[r]    (* A202542 *)
%t A202542 RealDigits[ Log[ (1+Sqrt[5])/2 ] / 3, 10, 99] // First (* _Jean-François Alcover_, Feb 27 2013 *)
%o A202542 (PARI) log((sqrt(5)+1)/2)/3 \\ _Charles R Greathouse IV_, May 14 2019
%Y A202542 Cf. A202537.
%K A202542 nonn,cons
%O A202542 0,2
%A A202542 _Clark Kimberling_, Dec 21 2011