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%I #28 Oct 26 2014 17:54:15
%S 6,8,5,9,4,7,0,3,5,1,6,7,4,2,8,4,8,1,8,7,5,7,3,5,9,6,1,9,8,0,4,1,7,3,
%T 5,8,7,4,8,8,6,2,1,4,1,8,7,0,3,0,1,5,0,6,7,0,1,8,6,6,8,5,8,1,7,0,3,0,
%U 1,8,7,6,7,1,4,6,9,5,7,3,8,5,6,1,7,8,3,7,3,7,0,1,6,5,9,1,1,1,0,4,8,9,1,5,0
%N Decimal expansion of the power tower of Euler constant gamma.
%H Stanislav Sykora, <a href="/A231095/b231095.txt">Table of n, a(n) for n = 0..2000</a>
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Euler_constant">Euler-Mascheroni constant</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 In general, for 1/E^E <= c < 1, c^c^c^... = LambertW(log(1/c))/log(1/c). Hence, this number is LambertW(log(1/gamma))/log(1/gamma).
%e 0.685947035167428481875735 ...
%p evalf(-LambertW(-log(gamma))/log(gamma), 120); # _Vaclav Kotesovec_, Oct 26 2014
%t c = EulerGamma; RealDigits[ ProductLog[-Log[c]]/Log[c], 10, 111] (* _Robert G. Wilson v_, Oct 24 2014 *)
%o (PARI) -lambertw(-log(Euler))/log(Euler)
%Y Cf. A001620.
%K nonn,cons
%O 0,1
%A _Stanislav Sykora_, Nov 03 2013
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