

A159825


Continued fraction for e^e^e A073227.


5



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
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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", n1, " ", 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



