This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A080219 #26 Feb 16 2025 08:32:48
%S A080219 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 A080219 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 A080219 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 A080219 Decimal expansion of exponential factorial constant Sum_{n>=1} 1/A049384(n).
%C A080219 This is a Liouville number and therefore transcendental.
%D A080219 Contributed by Jonathan Sondow.
%H A080219 J. Sondow, <a href="https://mathworld.wolfram.com/ExponentialFactorial.html">MathWorld: Exponential Factorial</a>
%H A080219 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 A080219 Wikipedia, <a href="https://en.wikipedia.org/wiki/Exponential_factorial">Exponential factorial</a>
%H A080219 Wikipedia, <a href="https://en.wikipedia.org/wiki/Liouville_number">Liouville number</a>
%H A080219 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>
%e A080219 1/1 + 1/2 + 1/9 + 1/262144 + ... = 1.611114925808376736111...
%t A080219 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 A080219 Cf. A049384, A167155.
%K A080219 nonn,cons
%O A080219 1,2
%A A080219 _Eric W. Weisstein_, Feb 06 2003