10/20/2008, 11:49 PM
Thanks for asking, Martin. I'm working with a function from N to N whose value at 1 is 2, its value at 2 is 7, and its value at 3 is A(A(A(61,61),A(61,61)), A(A(61,61),A(61,61))). I know A(61,61) is somewhat large, but I thought maybe someone with enough ram could pound it out so it would be more clear that (A(61,61), A(61,61)) is just a 2-tuple and so makes a valid argument for the next A in the nest
f(4) is
A(A(A(A(A(A(A(A(A(4,4),A(4,4)), A(A(4,4),A(4,4))), A(A(A(4,4),A(4,4)), A(A(4,4),A(4,4)))), A(A(A(A(4,4),A(4,4)), A(A(4,4),A(4,4))), A(A(A(4,4),A(4,4)), A(A(4,4),A(4,4))))), A(A(A(A(A(4,4),A(4,4)), A(A(4,4),A(4,4))), A(A(A(4,4),A(4,4)), A(A(4,4),A(4,4)))), A(A(A(A(4,4),A(4,4)), A(A(4,4),A(4,4))), A(A(A(4,4),A(4,4)), A(A(4,4),A(4,4)))))), A(A(A(A(A(A(4,4),A(4,4)), A(A(4,4),A(4,4))), A(A(A(4,4),A(4,4)), A(A(4,4),A(4,4)))), A(A(A(A(4,4),A(4,4)), A(A(4,4),A(4,4))), A(A(A(4,4),A(4,4)), A(A(4,4),A(4,4))))), A(A(A(A(A(4,4),A(4,4)), A(A(4,4),A(4,4))), A(A(A(4,4),A(4,4)), A(A(4,4),A(4,4)))), A(A(A(A(4,4),A(4,4)), A(A(4,4),A(4,4))), A(A(A(4,4),A(4,4)), A(A(4,4),A(4,4))))))), A(A(A(A(A(A(A(4,4),A(4,4)), A(A(4,4),A(4,4))), A(A(A(4,4),A(4,4)), A(A(4,4),A(4,4)))), A(A(A(A(4,4),A(4,4)), A(A(4,4),A(4,4))), A(A(A(4,4),A(4,4)), A(A(4,4),A(4,4))))), A(A(A(A(A(4,4),A(4,4)), A(A(4,4),A(4,4))), A(A(A(4,4),A(4,4)), A(A(4,4),A(4,4)))), A(A(A(A(4,4),A(4,4)), A(A(4,4),A(4,4))), A(A(A(4,4),A(4,4)), A(A(4,4),A(4,4)))))), A(A(A(A(A(A(4,4),A(4,4)), A(A(4,4),A(4,4))), A(A(A(4,4),A(4,4)), A(A(4,4),A(4,4)))), A(A(A(A(4,4),A(4,4)), A(A(4,4),A(4,4))), A(A(A(4,4),A(4,4)), A(A(4,4),A(4,4))))), A(A(A(A(A(4,4),A(4,4)), A(A(4,4),A(4,4))), A(A(A(4,4),A(4,4)), A(A(4,4),A(4,4)))), A(A(A(A(4,4),A(4,4)), A(A(4,4),A(4,4))), A(A(A(4,4),A(4,4)), A(A(4,4),A(4,4)))))))), A(A(A(A(A(A(A(A(4,4),A(4,4)), A(A(4,4),A(4,4))), A(A(A(4,4),A(4,4)), A(A(4,4),A(4,4)))), A(A(A(A(4,4),A(4,4)), A(A(4,4),A(4,4))), A(A(A(4,4),A(4,4)), A(A(4,4),A(4,4))))), A(A(A(A(A(4,4),A(4,4)), A(A(4,4),A(4,4))), A(A(A(4,4),A(4,4)), A(A(4,4),A(4,4)))), A(A(A(A(4,4),A(4,4)), A(A(4,4),A(4,4))), A(A(A(4,4),A(4,4)), A(A(4,4),A(4,4)))))), A(A(A(A(A(A(4,4),A(4,4)), A(A(4,4),A(4,4))), A(A(A(4,4),A(4,4)), A(A(4,4),A(4,4)))), A(A(A(A(4,4),A(4,4)), A(A(4,4),A(4,4))), A(A(A(4,4),A(4,4)), A(A(4,4),A(4,4))))), A(A(A(A(A(4,4),A(4,4)), A(A(4,4),A(4,4))), A(A(A(4,4),A(4,4)), A(A(4,4),A(4,4)))), A(A(A(A(4,4),A(4,4)), A(A(4,4),A(4,4))), A(A(A(4,4),A(4,4)), A(A(4,4),A(4,4))))))), A(A(A(A(A(A(A(4,4),A(4,4)), A(A(4,4),A(4,4))), A(A(A(4,4),A(4,4)), A(A(4,4),A(4,4)))), A(A(A(A(4,4),A(4,4)), A(A(4,4),A(4,4))), A(A(A(4,4),A(4,4)), A(A(4,4),A(4,4))))), A(A(A(A(A(4,4),A(4,4)), A(A(4,4),A(4,4))), A(A(A(4,4),A(4,4)), A(A(4,4),A(4,4)))), A(A(A(A(4,4),A(4,4)), A(A(4,4),A(4,4))), A(A(A(4,4),A(4,4)), A(A(4,4),A(4,4)))))), A(A(A(A(A(A(4,4),A(4,4)), A(A(4,4),A(4,4))), A(A(A(4,4),A(4,4)), A(A(4,4),A(4,4)))), A(A(A(A(4,4),A(4,4)), A(A(4,4),A(4,4))), A(A(A(4,4),A(4,4)), A(A(4,4),A(4,4))))), A(A(A(A(A(4,4),A(4,4)), A(A(4,4),A(4,4))), A(A(A(4,4),A(4,4)), A(A(4,4),A(4,4)))), A(A(A(A(4,4),A(4,4)), A(A(4,4),A(4,4))), A(A(A(4,4),A(4,4)), A(A(4,4),A(4,4)))))))))
f(4) is
A(A(A(A(A(A(A(A(A(4,4),A(4,4)), A(A(4,4),A(4,4))), A(A(A(4,4),A(4,4)), A(A(4,4),A(4,4)))), A(A(A(A(4,4),A(4,4)), A(A(4,4),A(4,4))), A(A(A(4,4),A(4,4)), A(A(4,4),A(4,4))))), A(A(A(A(A(4,4),A(4,4)), A(A(4,4),A(4,4))), A(A(A(4,4),A(4,4)), A(A(4,4),A(4,4)))), A(A(A(A(4,4),A(4,4)), A(A(4,4),A(4,4))), A(A(A(4,4),A(4,4)), A(A(4,4),A(4,4)))))), A(A(A(A(A(A(4,4),A(4,4)), A(A(4,4),A(4,4))), A(A(A(4,4),A(4,4)), A(A(4,4),A(4,4)))), A(A(A(A(4,4),A(4,4)), A(A(4,4),A(4,4))), A(A(A(4,4),A(4,4)), A(A(4,4),A(4,4))))), A(A(A(A(A(4,4),A(4,4)), A(A(4,4),A(4,4))), A(A(A(4,4),A(4,4)), A(A(4,4),A(4,4)))), A(A(A(A(4,4),A(4,4)), A(A(4,4),A(4,4))), A(A(A(4,4),A(4,4)), A(A(4,4),A(4,4))))))), A(A(A(A(A(A(A(4,4),A(4,4)), A(A(4,4),A(4,4))), A(A(A(4,4),A(4,4)), A(A(4,4),A(4,4)))), A(A(A(A(4,4),A(4,4)), A(A(4,4),A(4,4))), A(A(A(4,4),A(4,4)), A(A(4,4),A(4,4))))), A(A(A(A(A(4,4),A(4,4)), A(A(4,4),A(4,4))), A(A(A(4,4),A(4,4)), A(A(4,4),A(4,4)))), A(A(A(A(4,4),A(4,4)), A(A(4,4),A(4,4))), A(A(A(4,4),A(4,4)), A(A(4,4),A(4,4)))))), A(A(A(A(A(A(4,4),A(4,4)), A(A(4,4),A(4,4))), A(A(A(4,4),A(4,4)), A(A(4,4),A(4,4)))), A(A(A(A(4,4),A(4,4)), A(A(4,4),A(4,4))), A(A(A(4,4),A(4,4)), A(A(4,4),A(4,4))))), A(A(A(A(A(4,4),A(4,4)), A(A(4,4),A(4,4))), A(A(A(4,4),A(4,4)), A(A(4,4),A(4,4)))), A(A(A(A(4,4),A(4,4)), A(A(4,4),A(4,4))), A(A(A(4,4),A(4,4)), A(A(4,4),A(4,4)))))))), A(A(A(A(A(A(A(A(4,4),A(4,4)), A(A(4,4),A(4,4))), A(A(A(4,4),A(4,4)), A(A(4,4),A(4,4)))), A(A(A(A(4,4),A(4,4)), A(A(4,4),A(4,4))), A(A(A(4,4),A(4,4)), A(A(4,4),A(4,4))))), A(A(A(A(A(4,4),A(4,4)), A(A(4,4),A(4,4))), A(A(A(4,4),A(4,4)), A(A(4,4),A(4,4)))), A(A(A(A(4,4),A(4,4)), A(A(4,4),A(4,4))), A(A(A(4,4),A(4,4)), A(A(4,4),A(4,4)))))), A(A(A(A(A(A(4,4),A(4,4)), A(A(4,4),A(4,4))), A(A(A(4,4),A(4,4)), A(A(4,4),A(4,4)))), A(A(A(A(4,4),A(4,4)), A(A(4,4),A(4,4))), A(A(A(4,4),A(4,4)), A(A(4,4),A(4,4))))), A(A(A(A(A(4,4),A(4,4)), A(A(4,4),A(4,4))), A(A(A(4,4),A(4,4)), A(A(4,4),A(4,4)))), A(A(A(A(4,4),A(4,4)), A(A(4,4),A(4,4))), A(A(A(4,4),A(4,4)), A(A(4,4),A(4,4))))))), A(A(A(A(A(A(A(4,4),A(4,4)), A(A(4,4),A(4,4))), A(A(A(4,4),A(4,4)), A(A(4,4),A(4,4)))), A(A(A(A(4,4),A(4,4)), A(A(4,4),A(4,4))), A(A(A(4,4),A(4,4)), A(A(4,4),A(4,4))))), A(A(A(A(A(4,4),A(4,4)), A(A(4,4),A(4,4))), A(A(A(4,4),A(4,4)), A(A(4,4),A(4,4)))), A(A(A(A(4,4),A(4,4)), A(A(4,4),A(4,4))), A(A(A(4,4),A(4,4)), A(A(4,4),A(4,4)))))), A(A(A(A(A(A(4,4),A(4,4)), A(A(4,4),A(4,4))), A(A(A(4,4),A(4,4)), A(A(4,4),A(4,4)))), A(A(A(A(4,4),A(4,4)), A(A(4,4),A(4,4))), A(A(A(4,4),A(4,4)), A(A(4,4),A(4,4))))), A(A(A(A(A(4,4),A(4,4)), A(A(4,4),A(4,4))), A(A(A(4,4),A(4,4)), A(A(4,4),A(4,4)))), A(A(A(A(4,4),A(4,4)), A(A(4,4),A(4,4))), A(A(A(4,4),A(4,4)), A(A(4,4),A(4,4)))))))))