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

1,1

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}

Links

Table of n, a(n) for n=1..4.

Formula

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

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}] ]

Crossrefs

Cf. A079365, A124027.

Sequence in context: A151581 A145263 A185821 * A125542 A349876 A349896

Adjacent sequences: A133245 A133246 A133247 * A133249 A133250 A133251

Keyword

nonn,uned

Author

Roger L. Bagula, Oct 14 2007

Status

approved