A225064 -id:A225064 - cp's OEIS frontend

A056072 a(n) = floor(e^e^ ... ^e), with n e's.

1, 2, 15, 3814279

Offset: 0

Robert G. Wilson v, Jul 26 2000

nonn

The next term is too large to include.
From Vladimir Reshetnikov, Apr 27 2013: (Start)
a(4) = 2331504399007195462289689911...2579139884667434294745087021 (1656521 decimal digits in total), given by initial segment of A085667.
a(5) has more than 10^10^6 decimal digits.
a(6) has more than 10^10^10^6 decimal digits. (End)

Cf. A001113, A004002, A003417, A064107, A159825, A073226, A073227, A085667, A096232, A225064, A225053.

p:= n-> `if`(n=0, 1, exp(1)^p(n-1)):
a:= n-> floor(p(n)):
seq(a(n), n=0..3);  # Alois P. Heinz, Jul 20 2024

Floor[NestList[Exp, 1, 3]] (* Vladimir Reshetnikov, Apr 29 2013 *)

A056072(n,f=floor)=f(exp(if(n>0,A056072(n-1,x->x))))  \\ M. F. Hasler, May 01 2013

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

Original entry on oeis.org

1, 6, 9, 4

Offset: 1

Vladimir Reshetnikov, Apr 25 2013

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.

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

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

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

A056072 yields the first term of the continued fraction.

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

cp's OEIS Frontend

A056072 a(n) = floor(e^e^ ... ^e), with n e's.

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