A080219 Decimal expansion of exponential factorial constant Sum_{n>=1} 1/A049384(n).

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, 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, 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

Offset: 1

Author

Eric W. Weisstein, Feb 06 2003

Keywords

• nonn
• cons

Comments

This is a Liouville number and therefore transcendental.

Examples

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

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
• Index entries for transcendental numbers

Crossrefs

Cf. A049384, A167155.

Programs

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 *)