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

1, 6, 9, 4

Offset: 1

Author

Vladimir Reshetnikov, Apr 25 2013

Keywords

• nonn
• hard
• more

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.

Examples

			a(3) = 9 because floor(1/frac(e^e^e)) = 9, since e^e^e ~ 3814279.10476.
		

Links

• Eric Weisstein's World of Mathematics, e.
• Eric Weisstein's World of Mathematics, Power Tower
• Wikipedia, Tetration, Open questions

Crossrefs

Cf. A003417, A064107, A159825, A225064, A004002.

A056072 yields the first term of the continued fraction.

Programs

Mathematica

$MaxExtraPrecision = Infinity; terms = 4; Map[Function[x, ContinuedFraction[x, 2][[2]]], NestList[Exp, E, terms - 1]]