User blog comment:Maxywaxy/Do any functions reach this growth rate?/@comment-35870936-20181213051641

1: TREE(n) is a good example.

2: Depends what you mean by a "known" growth rate. If you mean "known" as in "we know it's growth rate in the FGH", then the strongest function would probably be f_a(n) where a is the largest ordinal we have a notation for in the FGH. If you want to be very esoteric, then we can use one of Michael Rathjen's OCFs, and we can let a be the ordinal limit of it (which will be crazy big).

3: Exact same as question 2. If there was a multi-argument function (call it f) that is stronger, then we can just define a function g(n)=f(n,100,100...100) assuming the first argument of f is the most important one (if it's not, then just change the order of the arguments).

4: The busy beaver function.