IMO you can't win big number competitions by such a low-level approach. At least notice that the concept of "deepest iterator in 1000 characters" is itself math

IMO you can't win big number competitions by such a low-level approach. At least notice that the concept of "deepest iterator in 1000 characters" is itself mathematically definable, and define it as D(1000) or something. Then try to find connections between that and BB numbers... Coming up with the "highest paradigm function" is the important part of the challenge, iteration is unnoticeable by comparison.