A004147 Number of n-state Turing machines which halt.

32, 9784, 7571840, 11140566368

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• nice
• hard
• bref

Comments

This sequence is noncomputable, because it could be used to solve the halting problem. In fact, it is of the same degree of difficulty as the halting problem. - David Diamondstone (skeptical.scientist(AT)gmail.com), Dec 28 2007

References

• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• J. P. Jones, Recursive undecidability - an exposition, Amer. Math. Monthly, 81 (1974), 724-738.
• H. Marxen, Busy Beaver
• Michael Somos, Busy Beaver Turing Machine
• Michael Somos, Busy Beaver
• Index entries for sequences related to Busy Beaver problem

Crossrefs

Cf. A028444, A052200.

Extensions

More terms from David Diamondstone (skeptical.scientist(AT)gmail.com), Dec 28 2007

a(4) from Jonathan Lee, who enumerated all 25.6 billion 4-state machines up to 107 steps, Mar 05 2016