OFFSET
0,1
COMMENTS
The common hyperoperation sequence is defined as follows: hyper-0 = zeration, hyper-1 = addition, hyper-2 = multiplication, hyper-3 = exponentiation, hyper-4 = tetration, and so on...
Thus e[0]e = e + 2, e[1]e = 2*e, e[2]e = e^2, e[3]e = e^e, and so on.
The fifth term of the twin sequence of the present one, floor(Pi[4]Pi), is much larger than 2075 and it is harder to calculate, while the integer part of e[4]Pi is 37149801960 (17.9 million times bigger than a(4)).
LINKS
Hellmuth Kneser, Reelle analytische Lösungen der Gleichung phi(phi(x)) = e^x und verwandter Funktionalgleichungen, J. reine angew. Math. 187, 56-67 (1950).
Sheldon Levenstein (user sheldonison), New fatou.gp program, Jul 10 2015, updated Aug 14 2019.
William Paulsen, Tetration.
William Paulsen, Tetration for complex bases, Advances in Computational Mathematics, Vol. 45, No. 1 (2019), pp. 243-267; ResearchGate link.
Wikipedia, Hyperoperation
FORMULA
a(n) = floor(e[n]e).
EXAMPLE
For n = 3, a(3) = floor(e[3]e) = floor(e^e) = 15.
CROSSREFS
KEYWORD
nonn,more,hard
AUTHOR
Marco Ripà, Apr 08 2022
STATUS
approved