A064107 - OEIS

%I #41 Aug 05 2024 12:46:13

%S 15,6,2,13,1,3,6,2,1,1,5,1,1,1,9,4,1,1,1,6,7,1,2,4,1,2,2,24,1,2,4,56,

%T 1,1,2,4,1,75,1,5,1,2,2,1,137,2,2,97,3,16,1,1,1,1,3,5,12,1,1,2,1,53,1,

%U 2,5,3,2,4,1,2,1,39,1,2,1,4,1,11,1,5,5,1,4,1,17,12,4,82,1,4,6,25,3,2,3

%N Continued fraction quotients for e^e = 15.15426224... (A073226).

%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="/A064107/b064107.txt">Table of n, a(n) for n = 0..19999</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/TranscendentalNumber.html">Transcendental Number</a>.

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/List_of_unsolved_problems_in_mathematics#Analysis">List of unsolved problems in mathematics, Analysis</a>.

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Irrational_number#Open_questions">Irrational number, Open questions</a>.

%e 15.154262241479264189760430... = 15 + 1/(6 + 1/(2 + 1/(13 + 1/(1 + ...)))). - _Harry J. Smith_, Apr 30 2009

%p with(numtheory): cfrac(evalf((exp(1))^(exp(1)),2560),256,'quotients');

%t ContinuedFraction[E^E,100] (* _Harvey P. Dale_, Sep 29 2012 *)

%o (PARI) { allocatemem(932245000); default(realprecision, 21000); x=contfrac(exp(exp(1))); for (n=1, 20000, write("b064107.txt", n-1, " ", x[n])); } \\ _Harry J. Smith_, Apr 30 2009

%Y Cf. A058287, A058288, A073226 (decimal expansion), A159825.

%K cofr,nonn

%O 0,1

%A _Labos Elemer_, Sep 17 2001

%E Offset changed by _Andrew Howroyd_, Aug 05 2024