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

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, 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, 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

Offset: 0

Author

Clark Kimberling, Dec 21 2011

Keywords

• nonn
• cons

Comments

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

Examples

			x=0.1604039416865344824992529711414561410450614447...
		

Links

• Index entries for transcendental numbers

Crossrefs

Cf. A202537.

Programs

Mathematica

u = 3; v = 3;
f[x_] := E^(u*x) - E^(-v*x); g[x_] := 1
Plot[{f[x], g[x]}, {x, -1, 1}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, .2, .3}, WorkingPrecision -> 110]
RealDigits[r]    (* A202542 *)
RealDigits[ Log[ (1+Sqrt[5])/2 ] / 3, 10, 99] // First (* Jean-François Alcover, Feb 27 2013 *)

PARI

log((sqrt(5)+1)/2)/3 \\ Charles R Greathouse IV, May 14 2019