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 A225053 Second terms of continued fractions for power towers e, e^e, e^e^e, ... 4
 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: A367730 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

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Last modified July 16 15:42 EDT 2024. Contains 374353 sequences. (Running on oeis4.)