A202495 Decimal expansion of x satisfying x = e^(-2*Pi*x).

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

Offset: 0

Author

Clark Kimberling, Dec 20 2011

Keywords

• nonn
• cons

Comments

See A202348 for a guide to related sequences. The Mathematica program includes a graph.

Examples

			x=0.232313382555181622895525466809054699600655...
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A000796, A001113, A202348.

Programs

Maple

evalf(LambertW(2*Pi)/(2*Pi), 145);  # Alois P. Heinz, Feb 26 2020

Mathematica

u = -2*Pi; v = 0;
f[x_] := x; g[x_] := E^(u*x + v)
Plot[{f[x], g[x]}, {x, 0, .5}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, .2, .3}, WorkingPrecision -> 110]
RealDigits[r]    (* A202357 *)
RealDigits[ ProductLog[2*Pi]/(2*Pi), 10, 99] // First (* Jean-François Alcover, Feb 19 2013 *)

Formula

Equals LambertW(2*Pi)/(2*Pi). - Alois P. Heinz, Feb 26 2020