User blog comment:Superlirarder/my extensions/@comment-44079442-20191206043747

I had actually contemplated the booga extension before, only with slightly different names, and even went further by diagonalization (that is, defining a prefix whose sequence would be booga(2), trooga(3), quatrooga(4), and so on). Booga- has a growth rate of f_w(n) in the fast-growing hierarchy, while trooga- is roughly equivalent to f_w+1, quatrooga is equivalent to f_w+2, quooga is equivalent to f_w+3, and so on. As an example, quatrooga(2) is equal to trooga(trooga(2)), which is booga applied to 4^4^4^4 that many times, which is already much larger than Graham's number, and the last 6 digits of that number are ...143296.