OFFSET
1,2
COMMENTS
This is a Liouville number and therefore transcendental.
REFERENCES
Contributed by Jonathan Sondow.
LINKS
J. Sondow, MathWorld: Exponential Factorial
J. Sondow, Irrationality measures, irrationality bases, and a theorem of Jarnik, arXiv:math/0406300 [math.NT], 2004; see L_4 in Example 4.
Wikipedia, Exponential factorial
Wikipedia, Liouville number
EXAMPLE
1/1 + 1/2 + 1/9 + 1/262144 + ... = 1.611114925808376736111...
MATHEMATICA
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 *)
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Eric W. Weisstein, Feb 06 2003
STATUS
approved