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Decimal expansion of exponential factorial constant Sum_{n>=1} 1/A049384(n).
2

%I #25 May 14 2019 21:35:54

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

%T 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,

%U 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1

%N Decimal expansion of exponential factorial constant Sum_{n>=1} 1/A049384(n).

%C This is a Liouville number and therefore transcendental.

%D Contributed by Jonathan Sondow.

%H J. Sondow, <a href="http://mathworld.wolfram.com/ExponentialFactorial.html">MathWorld: Exponential Factorial</a>

%H J. Sondow, <a href="http://arXiv.org/abs/math.NT/0406300">Irrationality measures, irrationality bases, and a theorem of Jarnik</a>, arXiv:math/0406300 [math.NT], 2004; see L_4 in Example 4.

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Exponential_factorial">Exponential factorial</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Liouville_number">Liouville number</a>

%H <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>

%e 1/1 + 1/2 + 1/9 + 1/262144 + ... = 1.611114925808376736111...

%t eFac[1] = 1; eFac[n_] := eFac[n] = n^eFac[n-1]; Clear[s]; s[m_] := s[m] = RealDigits[Sum[1/eFac[n], {n, 1, m}], 10, 100] // First; s[m = 1]; While[s[m] != s[m - 1], m++]; s[m] (* _Jean-François Alcover_, Feb 08 2013 *)

%Y Cf. A049384, A167155.

%K nonn,cons

%O 1,2

%A _Eric W. Weisstein_, Feb 06 2003