User blog comment:Deedlit11/The slow-growing hierarchy and other hierarchies/@comment-25418284-20130313225434

I sat down with \(B_\alpha(p)\) for a while and found what I believe is an exact value for \(B_{\Gamma_0}(p)\):

\[p \langle p \langle p \langle \cdots p + 1 \cdots \rangle p + 1 \rangle p + 1 \rangle p\]

with \(p + 1\) layers. So my guess was correct &mdash; this really is quite close to \(p \langle \langle 1 \rangle \rangle p\).