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A225053 Second terms of continued fractions for power towers e, e^e, e^e^e, ... 3
1, 6, 9, 4 (list; graph; refs; listen; history; text; internal format)
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: A239068 A259833 A085138 * A215483 A153872 A242208

Adjacent sequences:  A225050 A225051 A225052 * A225054 A225055 A225056

KEYWORD

nonn,hard,more

AUTHOR

Vladimir Reshetnikov, Apr 25 2013

STATUS

approved

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Last modified June 18 16:46 EDT 2019. Contains 324214 sequences. (Running on oeis4.)