Deriving tetration from selfroot?

[Ivars]

But if we add one more supperroot level (5th) it changes a bit:

3^3^3^3^3 = 3^3^(3^3) = 4,43426E+38 = 27^27
2^2^2^2^2= 2^(2^(2^2) = 65536

So 5 times exponentiated 2 =2[4]4; But 5 times exponenetiated 3 equals something that has no name -at least I do not know it - it is smaller(slower) then n=4 tetration of 3 but bigger(faster) than 4 times applied exponentation of 3.

Moving to 6th superroot with 2:

2^2^2^2^2^2 = 2^2^(2^(2^2)) = 4294967296= 4^4^4
3^3^3^3^3^3= 3^3^3^(3^3) = 8,719E+115

6 times exponentiation of 2 is smaller then 5 times tetration of 2 but equals something applied to 5 2-es that I have no name of.
6 times expnentiation of 3 equals 5 times something.

Ivars