1,1

Row sums give A140087.

What is interesting here is that Richard Jeffery and Gregory Chaitin seem to reach completely different conclusions about the halting problem.

G. J. Chaitin, Algorithmic Information Theory, Cambridge Univ. Press, 1987, page 169.

G. J. Chaitin, Meta Math, The Quest for Omega,Vintage Books,2005, page 29 ff.

Richard Jeffrey, Formal Logic: Its Scope and Limits. 3rd ed. McGraw Hill, 1990. ISBN 0-07-032357-7, pages 134-5

f(n_, 1) := n + 1; f[n_, 2] := Undecided; f[n_, 3] := If[n == 0, 0, n - 1]; f[n_, 4] := If[n == 0, Undecided, n - 1]; f[n_, 5] := 0; f[n_, 6] := Undecided; f[n_, m_] := f[n, 1 + Mod[m, 6]]; h(m,n)=If[ program halts/f(n,m) is decided,0,1]

{1},

{1, 0},

{1, 0, 1},

{1, 0, 1, 1},

{1, 0, 1, 1, 1},

{1, 0, 1, 1, 1, 0},

{1, 0, 1, 1, 1, 0, 0},

{1, 0, 1, 1, 1, 0, 0, 1},

{1, 0, 1, 1, 1, 0, 0, 1, 1},

{1, 0, 1, 1, 1, 0, 0, 1, 1, 1}

(* use 10^50 as a symbol for " Undecided" or undefined.*) f[n_, 1] := n + 1; f[n_, 2] := 10^50; f[n_, 3] := If[n == 0, 0, n - 1]; f[n_, 4] := If[n == 0, 10^50, n - 1]; f[n_, 5] := 0; f[n_, 6] := 10^50; f[n_, m_] := f[n, 1 + Mod[m, 6]]; h[m_, n_] := If[f[n, m] == 10^50, 0, 1]; a = Table[Table[h[m, n], {m, 1, n}], {n, 1, 10}]; Flatten[a]

Cf. A124027, A072851.

Adjacent sequences: A136666 A136667 A136668 this_sequence A136670 A136671 A136672

Sequence in context: A108336 A118268 A143220 this_sequence A103842 A065535 A093719

nonn,uned,tabl,more,obsc

Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Apr 03 2008

The definition of this sequence is not clear to me. Furthermore, the rows appear to converge to a certain binary sequence. If so, there should be a cross-reference to it (or it should be added if it is not presently in the OEIS). - njas, Jun 04 2008