$\log^k(n) = \log(\log(\log(...\log(n))));$


Let $f(n)$ = smallest $k$, s.t. $\log^k(n) \leq 1$


Is there known name for function $f$ ? Or it's an instance of some known function ?


Basically I want to know if anyone else also treating $O(f(n))$ as good as $O(1)$.



Is there special name for this function ?, $f(n)$ = smallest $k$, s.t. $\log^k(n) \leq 1$
This is the [iterated logarithm](https://en.wikipedia.org/wiki/Iterated_logarithm) function, commonly denoted $\log^\*(n)$.


It happens to come up from time to time in the analysis of various algorithms; while it grows extremely slowly, and is basically a constant for most practical purposes, it is still an unbounded function, and you cannot present it as being $O(1)$.


