I was trying to prove (or to find a counterexample) of the following inequality:
As I coudn't find a proof/counterexample, I tested some numbers and could see it working up to $n=12$. Does anyone have a proof/counterexample of it? I've tried to pass the $\log_2$ in both sides, in order to use properties of $\log$, but I could't find anything better. Any help will be appreciated.