A231096 - OEIS

%I #20 Apr 24 2016 12:45:42

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

%T 3,2,4,8,2,8,4,5,8,4,3,9,4,3,4,4,6,0,9,6,9,0,0,8,9,5,1,4,2,9,9,1,6,0,

%U 1,5,9,7,2,6,0,9,6,7,2,7,3,3,9,9,0,5,9,4,6,5,3,5,7,2,9,5,5,6,1,3,9,2,5,3,2

%N Decimal expansion of the power tower of the inverse of golden ratio.

%C Also the only solution of x*phi^x = 1.

%H Stanislav Sykora, <a href="/A231096/b231096.txt">Table of n, a(n) for n = 0..1999</a>

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Lambert_W_function">Lambert W function</a>

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Tetration">Tetration</a>

%F When 1/E^E <= c < 1, then c^c^c^... = LambertW(log(1/c))/log(1/c).

%e 0.710439287156503188669345...

%t RealDigits[ LambertW[ Log[ GoldenRatio]]/Log[ GoldenRatio], 10, 111][[1]] (* _Robert G. Wilson v_, Feb 11 2015 *)

%o (PARI) lambertw(log(phi))/log(phi)

%Y Cf. A094214 (1/phi), A001622 (phi), A231095 (power tower of Gamma).

%K nonn,cons

%O 0,1

%A _Stanislav Sykora_, Nov 04 2013