User blog comment:Flavio61/Louis Epstein number list/@comment-27173506-20160118190252/@comment-27173506-20160118193321

I will use a "v" for underlined u's. Nothing's unclear, I just misread something.

n u n~n^^n~f_4(n)

n uu n=n u n u n~f_4(f_4(n))

n nu n~f_4n(n)=f_5(n)

n v n~f_4f_4(n)(n)~f_5(f_4(n))

n vv n~f_4f_3(f_4(n))(n)~f_5(f_4(f_3(n)) (This is due to exponentiation being about f_3(n))

n nv n~f_4f_4(f_4(n))~f_5(f_4(f_4(n))

n (u) n=n n n u nu n u n~f_4f_4(f_4(n))~f_5(f_4(f_4(n))

n n(un) n~f_5(f_5(n))

Ultrexing the number of nestings will bring you up to about f_5(f_5(f_4(n))), and the curly brackets bring you up to about f_5(f_5(f_5(n))).

So yes, about f_6(n), possibly even less. The thing is that like I said before, you're not treating each level as a function that you nest, but are applying the comparatively weak basic ultrex function each time. Using n mu x=n m-1u n m-1u n m-1u n...n m-1u n, we already reach f_w(n), because we're recursing over every last stage where the amount of the recursings is the number resulting from applying the function, and not recursing using a weak function.