Beeping busy beaver function

The beeping busy beaver function is a relative of the maximum shifts functionAaronson refers to the maximum shifts function as the "busy beaver function", a term which on this wiki usually refers to the sigma function. proposed by Scott Aaronson in a conversation with Harvey Friedmanhttps://www.scottaaronson.com/papers/bb.pdf (retrieved 2021-03-03). Define a beep state as a state that is only exited a finite amount of times. Then for a Turing machine M, b(M) is the number of the last step on which it exits a beep state. BBB(n) is the maximum value of b(M) if M is a n-state Turing machine.
This function grows strictly faster than the standard busy beaver function. In particular, it cannot be computed even with a first-order oracle machine. The beeping busy beaver function is thus an explicitly constructed function equivalent to the second-order busy beaver function in growth rate.
==Known values and bounds==
*BBB(1) = 1
*BBB(2) = 6
*BBB(3) ≥ 55
*BBB(4) ≥ 32779478Collatz-like behavior of Busy Beavers
*BBB(5) > 1014006https://bbchallenge.org/~pascal.michel/ha#bbb
==Footnotes==
==References==
Category:Functions
Category:Uncomputable
Category:Numbers_based_off_of_the_busy_beaver