A266092 Decimal expansion of the power tower of 1/sqrt(3): the real solution to 3^(x/2)*x = 1.
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, 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, 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
Offset: 0
Examples
(1/sqrt(3))^(1/sqrt(3))^(1/sqrt(3))^(1/sqrt(3))^… = 0.686026724536251319713006846182…
Links
- Eric Weisstein's World of Mathematics, Power Tower
- Eric Weisstein's World of Mathematics, Lambert W-Function
Programs
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Mathematica
RealDigits[(2 ProductLog[Log[3]/2])/Log[3], 10, 120][[1]]
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PARI
t=log(3)/2; lambertw(t)/t \\ Charles R Greathouse IV, Apr 18 2016
Formula
Equals 2*LambertW(log(3)/2)/log(3).