Proving a language is not decideable using a reduction from Busy Beaver?
Hint: Why is the busy beaver function difficult (rather, impossible) to compute? Consider the following algorithm: given $n$, run all $n$-state Turing machines, and whenever one of them halts, update your estimate on the maximum number of steps. Eventually you will have found $BB(n)$, but you wouldn't know, since some of your machines are still running. Will any of them terminate, or have you discovered $BB(n)$? The function $F(n)$ given to you in the question could help in that respect.