2×10^10^10^18,705,352 (“Wythagoras” 2014)
As you can see, the function is reasonably under control for n≤4, then “achieves liftoff” at n=5.
In my survey, inspired by a suggestion of Harvey Friedman, I defined a variant called Beeping Busy Beaver, or BBB. Define a
beeping Turing machine to be a TM that has a single designated state where it emits a “beep.” The
beeping number of such a machine M, denoted b(M), is the largest t such that M beeps on step t, or ∞ if there’s no finite maximum. Then BBB(n) is the largest finite value of b(M), among all n-state machines M.
Steven-weinberg
Nick-drozd
Harvey-friedman
Busy-beaver
Beeping-busy-beaver
Blanking-beaver
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