A159825 Continued fraction for e^e^e A073227.

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, 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, 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

Offset: 0

Author

Harry J. Smith, Apr 30 2009

Keywords

• nonn
• cofr
• easy

Comments

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

Examples

			3814279.104760220592209... = 3814279 + 1/(9 + 1/(1 + 1/(1 + 1/(4 + ...)))).
		

Links

• Harry J. Smith, Table of n, a(n) for n = 0..20000
• Eric Weisstein's World of Mathematics, Transcendental Number.
• Wikipedia, Irrational number, Open questions.

Crossrefs

Cf. A003417, A064107.

Programs

Mathematica

ContinuedFraction[E^E^E, 96] (* Vladimir Reshetnikov, Apr 27 2013 *)

PARI

{ allocatemem(932245000); default(realprecision, 21000); x=contfrac(exp(exp(exp(1)))); for (n=1, 20001, write("b159825.txt", n-1, " ", x[n])); }