A202538 Decimal expansion of the number x satisfying e^x-e^(-3x)=1.

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, 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, 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

Offset

0,1

Comments

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

Links

Table of n, a(n) for n=0..98.

Index entries for transcendental numbers

Example

x=0.32228461597103006003623548628913923545544311...

Mathematica

u = 1; v = 3;
f[x_] := E^(u*x) - E^(-v*x); g[x_] := 1
Plot[{f[x], g[x]}, {x, -2, 2}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, .3, .4}, WorkingPrecision -> 110]
RealDigits[r]  (* A202538 *)
RealDigits[ Log[ Root[#^4 - #^3 - 1&, 2]], 10, 99] // First (* Jean-François Alcover, Feb 27 2013 *)

Prog

(PARI) log(polrootsreal(x^4-x^3-1)[2]) \\ Charles R Greathouse IV, May 15 2019

Crossrefs

Cf. A202537.

Sequence in context: A134653 A090207 A364571 * A239736 A065437 A097721

Adjacent sequences: A202535 A202536 A202537 * A202539 A202540 A202541

Keyword

nonn,cons

Author

Clark Kimberling, Dec 21 2011

Status

approved