A133248 Provides a relationship between a representation of Lisp programs of length n and Chaitan's Omega: If[A124027(n)==0, then row sum of[A124027].

9, 5798, 2356779, 6536382

Offset: 1

Author

Roger L. Bagula, Oct 14 2007

Keywords

• nonn
• uned

Comments

If the first two rows of A124027 are left off, the wrong answer is given for the number of program representations necessary to be tested. My machine won't calculate to the next one at n=25. This line of reasoning also produces the sequence: Flatten[Table[If[c[[n]] == 1, n, {}], {n, 1, Length[c]}]] {7, 14, 20, 21, 25, 30, 31, 33, 37, 38, 39, 40, 41, 42, 45, 47, 48, 49, 51, 52, 53, 55, 60}

Crossrefs

Cf. A079365, A124027.

Programs

Mathematica

(*A079365*); c = {0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1,1, 0, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0,1, 0, 0, 0, 0, 1, 0, 0, 0, 0}; (*A124027*); p[0, x] = 0; p[1, x] = x; p[2, x] = 1; p[k_, x_] := p[k, x] = Sum[ p[j, x]*p[k - j, x], {j, 2, k - 1}]; Flatten[Table[If[c[[n + 1]] == 1, Sum[CoefficientList[p[n, x], x][[m]], {m, 1, Length[CoefficientList[p[n, x], x]]}], {}], {n, 0, 21}] ]

Formula

a(n) = If[A124027(m)==0, then row sum of[A124027](m)