User blog comment:Emlightened/Intro/@comment-1605058-20160109180510/@comment-27513631-20160109234737

My intention, if not my wording, was that F was defined recursively from F and PR functions, and nothing else. Obviously, this would exclude the busy beaver function etc., but the idea was for the creation of fast growing functions by some other means than arrays and structures. If you wanted to create a function by encoding a turing machine into PR functions, and have G come up with the result, then that would be fine. If you wanted to recreate TREE by encoding the bracket types into a bitstring, then that would be fine, too. If you wanted to do something more original, like encoding a variant of primitive sequence system into a number through prime factorisation and then iteratively reduce, then that would be great - the purpose was to inspire people to make fast-growing recursive functions that didn't rely on structures, but instead were unique or had a neat twist to them.

And, if you wanted to, everything up to $$f_{\omega^\omega}$$ can be made relatively trivially by defining the first argument of f to be n, the second one to be the number of iterations, and the rest to be powers of $$\omega$$.

The sentence: "The functions F and G such that all of the functions in the definition of F and G, are primitive recursive, or F itself, and F and G are defined recursively using only these functions." would have been more accurate.