OFFSET
0,1
COMMENTS
Next term is too big to include.
a(n+1) = a(n) written in base 3 and read as if in base 27 (and recorded in base 10).
Number of distinct n-ary operators in a ternary logic. - Ross Drewe, Feb 13 2008
The next term has 116 digits. - Harvey P. Dale, Mar 28 2019
LINKS
Amiram Eldar, Table of n, a(n) for n = 0..6
FORMULA
a(n) = a(n-1)^3.
Sum_{n>=0} 1/a(n) = A383817. - Amiram Eldar, May 16 2025
From Andrea Pinos, Jun 08 2026: (Start)
3^(3^n) = 4*Product_{j=0..(n-1)} (Sum_{k=0..2} ((-1)^k*(3^(3^j))^k)) - 1;
3^(3^n) = 2*Product_{j=0..(n-1)} (Sum_{k=0..2} ((3^(3^j))^k)) + 1;
More generally: b^(b^n) = (b - 1)*Product_{j=0..(n-1)} (Sum_{k=0..(b-1)} ((b^(b^j))^k)) + 1. (End)
MATHEMATICA
NestList[#^3&, 3, 5] (* Harvey P. Dale, Mar 28 2019 *)
PROG
(Python)
print([3**(3**n) for n in range(5)]) # Michael S. Branicky, Mar 27 2021
CROSSREFS
KEYWORD
nonn,changed
AUTHOR
Henry Bottomley, Jul 12 2000
STATUS
approved