User blog comment:Eners49/New Notation Idea? (Attempt 2)/@comment-31966679-20180709175013

1- entry: \(f_{2}(n)\) or \(f_{3}(n)\) like you said.

2 - entry: around \(f_{\omega}(n)\) or \(f_{\omega + 1}(n)\). Roughly Graham's function

3-entry: around \(f_{\omega ^ {2}}(n)\)

Noting that my calculations may be incorrect because I'm not very good at googology or math in general.

However, I have a way you can generalize this.

\(\{a\} = a\underbrace{!! \ldots !}_a\)

\(\{a, b, \ldots, 1\} = \{a, b, \ldots\}\)



\(\{a, b, \ldots, c\} = \{\underbrace{\{\ldots \{a\} \ldots\}}_{a}, b - 1, \ldots, c\}\)

\(\{a, \ldots, b, 1, c, \ldots, d\} = \{a, \ldots, b, b, c - 1, \ldots, d\}\)

This could go all the way up to \(f_{\omega ^ {\omega}}(n)\) for n-entry arrays! And after that, you could even make a second function which diagonalizes over that, but for now stick with n-entry arrays.