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%I #20 Apr 18 2016 10:56:03
%S 6,8,6,0,2,6,7,2,4,5,3,6,2,5,1,3,1,9,7,1,3,0,0,6,8,4,6,1,8,2,2,3,8,1,
%T 5,9,5,0,3,3,2,4,2,3,7,7,6,2,3,4,3,4,0,2,4,1,7,6,7,1,9,1,6,7,0,0,4,0,
%U 2,9,0,5,8,1,8,7,5,4,8,4,8,7,7,6,4,2,8,1,5,7,8,6,8,9,3,9,8,2,6,3,8,0,6,6,8,6,9,9,3,5,2,8,3,3,2,4,8,9,6,7
%N Decimal expansion of the power tower of 1/sqrt(3): the real solution to 3^(x/2)*x = 1.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PowerTower.html">Power Tower</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/LambertW-Function.html"> Lambert W-Function</a>
%F Equals 2*LambertW(log(3)/2)/log(3).
%e (1/sqrt(3))^(1/sqrt(3))^(1/sqrt(3))^(1/sqrt(3))^… = 0.686026724536251319713006846182…
%t RealDigits[(2 ProductLog[Log[3]/2])/Log[3], 10, 120][[1]]
%o (PARI) t=log(3)/2; lambertw(t)/t \\ _Charles R Greathouse IV_, Apr 18 2016
%Y Cf. A020760, A030178, A073084, A073243, A231096.
%K nonn,cons
%O 0,1
%A _Ilya Gutkovskiy_, Dec 21 2015