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%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
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