A118874 A halting sequence: let f_n be the n-th recursive function, relative to the Godel numbering given in Cutland, then a(n) is f_n(n)+1 if the corresponding program halts on input n, 0 otherwise.

1, 3, 1, 4, 2, 1, 1, 0, 1, 12, 2, 1, 1, 1, 1, 16, 0, 19, 1, 21, 3, 2, 2, 0, 1, 1, 1, 1, 1, 1, 1, 32, 1, 0, 0, 36, 2, 1, 1, 0, 2, 45, 3, 2, 2, 2, 2, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 64, 1, 67, 1, 0, 0, 0, 0, 0, 1, 76, 2, 1, 1, 1, 1, 81, 0, 84, 2, 86, 4, 3, 3, 0, 2, 2, 2, 2, 2, 2, 2, 1, 1, 0, 0

Offset: 0

Author

Sam Alexander, May 24 2006

Keywords

• nonn

Comments

The prototypical example of a noncomputable sequence.

Examples

			Using Cutland's Godel numbering, 80 corresponds to the URM program "Z(1) J(1,1,1) S(1)", which clearly loops forever on any input, so a(80)=0. On the other hand, 17 corresponds to the URM program "S(1) T(1,1)", which, on input 17, produces 18. So a(17)=18+1=19.
		

References

• Nigel Cutland, "Computability: An introduction to recursive function theory". Cambridge University Press, 1980. p. 78.

Links

• Ramin Naimi, URM Simulator

Crossrefs

Cf. A004147, A028444, A052200, A060843, A081419.