User blog comment:Mh314159/Question about growth rate/@comment-39541634-20191107013022

In general, iterating a function N times, gets you to the next function in the FGH with argument N.

If we iterate an ω2-level function 100 times, the result will be roughly fω2+1(100).

If we iterate it a million times, we'll get fω2+1(1000000).

And if we iterate said function an fω2(n-1) times? The same rule still applies, so we get: fω2+1(fω2(n-1)) So that's a rough estimate for your answer. It's still only one level above ω2, because (for example) it's still smaller than fω2+2(3): fω2+2(3) = fω2+1(fω2+1(fω2+1(3)))  = fω2+1(fω2+1(something huge)) >> fω2+1(fω2(n-1)) for any reasonable n.