|
| |
|
|
A225053
|
|
Second terms of continued fractions for power towers e, e^e, e^e^e, ...
|
|
3
|
| |
|
|
|
OFFSET
|
1,2
|
|
|
COMMENTS
|
It was conjectured (but remains unproved) that none of the power towers e, e^e, e^e^e, ... are integers. If so, the corresponding continued fractions contain at least 2 terms. If the conjecture fails, let the corresponding a(n) = 0.
|
|
|
LINKS
|
Table of n, a(n) for n=1..4.
Eric Weisstein's World of Mathematics, e.
Eric Weisstein's World of Mathematics, Power Tower
Wikipedia, Tetration, Open questions
|
|
|
EXAMPLE
|
a(3) = 9 because floor(1/frac(e^e^e)) = 9, since e^e^e ~ 3814279.10476.
|
|
|
MATHEMATICA
|
$MaxExtraPrecision = Infinity; terms = 4; Map[Function[x, ContinuedFraction[x, 2][[2]]], NestList[Exp, E, terms - 1]]
|
|
|
CROSSREFS
|
Cf. A003417, A064107, A159825, A225064, A004002.
A056072 yields the first term of the continued fraction.
Sequence in context: A259833 A085138 A346176 * A341641 A215483 A153872
Adjacent sequences: A225050 A225051 A225052 * A225054 A225055 A225056
|
|
|
KEYWORD
|
nonn,hard,more
|
|
|
AUTHOR
|
Vladimir Reshetnikov, Apr 25 2013
|
|
|
STATUS
|
approved
|
| |
|
|
