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

0,1

Comments

It was conjectured (but remains unproved) that this sequence is infinite and aperiodic, but it is difficult to find who first posed this problem. - Vladimir Reshetnikov, Apr 27 2013

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

Example

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

Mathematica

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

Prog

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

Crossrefs

Cf. A003417, A064107.

Sequence in context: A175890 A083601 A209516 * A185533 A206413 A253869

Adjacent sequences: A159822 A159823 A159824 * A159826 A159827 A159828

Keyword

nonn,cofr,easy

Author

Harry J. Smith, Apr 30 2009

Status

approved