Follow-up question, assuming we define BB(n) = max number of 1s written to tape for a halting machine of n states.

Does it make sense to compare BB(n) against A333479(n)?

It seems like A333479(n) grows much faster... my mind is jumping to the classic "problem" of being able to construct a lambda term of size O(2^n) using only O(n) steps. For a Turing machine, writing a symbol requires at least one step. But for lambda, you can generate large terms very quickly.

(Of course, this isn't a fundamental issue with lambda calculus, and there are other notions of size that are more "realistic". But focusing on just lambda calculus normal form sizes, how do we resolve this?)