User blog comment:Primussupremus/Extended busy beaver or super sigma./@comment-29915175-20170406195949/@comment-30754445-20170407084955

Interesting question: can one prove any relation between the two versions of the BB function (besides the obvious fact that BBsteps(n) >= BBones(n))?

From the known values and bounds up to n=6, it seems that the former grows like the square of the latter (1, 6, 21, 107, 5E7, 7E36535 vs 1, 4, 6, 13, 4E3, 4E18267). And if such a relation can be proven, then we get a very interesting conclusion: For n>=7 both functions give nearly identical results (googologically speaking) since squaring a number like 10^10^10^10^10^7 has a completely negligible effect on its size.