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A225053
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Second terms of continued fractions for power towers e, e^e, e^e^e, ...
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3
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OFFSET
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1,2
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COMMENTS
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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.
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LINKS
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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
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EXAMPLE
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a(3) = 9 because floor(1/frac(e^e^e)) = 9, since e^e^e ~ 3814279.10476.
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MATHEMATICA
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$MaxExtraPrecision = Infinity; terms = 4; Map[Function[x, ContinuedFraction[x, 2][[2]]], NestList[Exp, E, terms - 1]]
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CROSSREFS
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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
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KEYWORD
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nonn,hard,more
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AUTHOR
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Vladimir Reshetnikov, Apr 25 2013
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STATUS
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approved
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