A064107 Continued fraction quotients for e^e = 15.15426224... (A073226).

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, 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, 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

Offset: 0

Author

Labos Elemer, Sep 17 2001

Keywords

• cofr
• nonn

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

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

Links

• Harry J. Smith, Table of n, a(n) for n = 0..19999
• Eric Weisstein's World of Mathematics, Transcendental Number.
• Wikipedia, List of unsolved problems in mathematics, Analysis.
• Wikipedia, Irrational number, Open questions.

Crossrefs

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

Programs

Maple

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

Mathematica

ContinuedFraction[E^E,100] (* Harvey P. Dale, Sep 29 2012 *)

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

Extensions

Offset changed by Andrew Howroyd, Aug 05 2024