A202495 - OEIS

%I #16 Feb 27 2020 14:56:58

%S 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,

%T 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,

%U 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

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

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

%H Alois P. Heinz, <a href="/A202495/b202495.txt">Table of n, a(n) for n = 0..10000</a>

%F Equals LambertW(2*Pi)/(2*Pi). - _Alois P. Heinz_, Feb 26 2020

%e x=0.232313382555181622895525466809054699600655...

%p evalf(LambertW(2*Pi)/(2*Pi), 145);  # _Alois P. Heinz_, Feb 26 2020

%t u = -2*Pi; v = 0;

%t f[x_] := x; g[x_] := E^(u*x + v)

%t Plot[{f[x], g[x]}, {x, 0, .5}, {AxesOrigin -> {0, 0}}]

%t r = x /. FindRoot[f[x] == g[x], {x, .2, .3}, WorkingPrecision -> 110]

%t RealDigits[r]    (* A202357 *)

%t RealDigits[ ProductLog[2*Pi]/(2*Pi), 10, 99] // First (* _Jean-François Alcover_, Feb 19 2013 *)

%Y Cf. A000796, A001113, A202348.

%K nonn,cons

%O 0,1

%A _Clark Kimberling_, Dec 20 2011