See my other comment: log* only conquers the second level of Knuth arrows, e ↑↑ n. But you can easily generalize log* , in a way that mirrors the way Knuth arro

See my other comment: log* only conquers the second level of Knuth arrows, e ↑↑ n. But you can easily generalize log* , in a way that mirrors the way Knuth arrows are constructed, and inverts them at any level. Say log*[1](n) = log(n) log*[k](n) = 0 if n <= 1 = 1 + log*[k](log*[k-1](n)) if n > 1 Then the k-th level is the inverse of the k-th level Knuth arrows, e ↑^k n -- that is, e ↑↑..↑ n, with k arrows.