A231095 - OEIS

%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