The OEIS is supported by the many generous donors to the OEIS Foundation.
Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.
Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.
%I #18 Jun 01 2024 10:01:33
%S 3814279,9,1,1,4,1,53,26,1,13,3,1,1,22,1,226,1,5,2,1,6,2,3,1,4,1,6,39,
%T 2,1,3,1,5,1,4,1,3,1,4,1,1,19,1,2,8899,5,2,2,1,3,3,2,2,2,1,1,3,5,1,6,
%U 10,2,1,2,1,1,1,2,2,4,1,10,2,6,1,5,6,2,4,2,1,2,1,1,1,3,2,2,1,1,11,7,3,1,4,4
%N Continued fraction for e^e^e A073227.
%C It was conjectured (but remains unproved) that this sequence is infinite and aperiodic, but it is difficult to determine who first posed this problem. - _Vladimir Reshetnikov_, Apr 27 2013
%H Harry J. Smith, <a href="/A159825/b159825.txt">Table of n, a(n) for n = 0..20000</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/TranscendentalNumber.html">Transcendental Number</a>.
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Irrational_number#Open_questions">Irrational number, Open questions</a>.
%e 3814279.104760220592209... = 3814279 + 1/(9 + 1/(1 + 1/(1 + 1/(4 + ...)))).
%t ContinuedFraction[E^E^E, 96] (* _Vladimir Reshetnikov_, Apr 27 2013 *)
%o (PARI) { allocatemem(932245000); default(realprecision, 21000); x=contfrac(exp(exp(exp(1)))); for (n=1, 20001, write("b159825.txt", n-1, " ", x[n])); }
%Y Cf. A003417, A064107.
%K nonn,cofr,easy
%O 0,1
%A _Harry J. Smith_, Apr 30 2009