T in T_(n, k) is a Turing machine with n states and k symbols;
States q, q+ in set Q_n of n distinct states (plus the Halt state;)
Symbols s, s+ in set S_k of k distinct symbols (0 as the blank symbol;)
Shift direction d+ in {LEFT, RIGHT} (NONE is excluded here;)
+ suffix meaning next and q+ = f(q, s), s+ = g(q, s), d+ = h(q, s).
This sequence is computable. On the other hand, the busy beaver numbers are noncomputable, found only by examining each of the many nstate Turing machine programs' halting.  Michael Joseph Halm, Apr 29 2003
From Daniel Forgues, Jun 06 2011: (Start)
RE: Busy beaver halting Turing machines:
H in H_(n, k) is a halting* Turing machine with n states and k symbols;
* (on a blank tape, all 0s, as input)
sigma(H) is the number of nonblank symbols left on the tape by H;
s(H) is the number of steps (or shifts in our case) taken by H;
Sigma(n, k) = max {sigma(H) : H is a halting Turing machine with n states and k symbols}
S(n, k) = max {s(H) : H is a halting Turing machine with n states and k symbols}
Cf. A028444 for Sigma(n, 2), A060843 for S(n, 2). (End)
