User blog comment:Ecl1psed276/Growth rate of oracle Turing machines/@comment-35470197-20190714085120/@comment-35870936-20190714191553

According to the Wikipedia page, Kleene's O gives a notation for exactly the recursive ordinals, which are bounded above by \(f_{\omega_1^{CK}}\). I don't know how a function based off of this could be "much bigger" than BB(n) as you say, becuase BB(n) also grows faster than \(f_\alpha\) for all recursive ordinals \(\alpha\).