A369412 Maximum length of a "normal" proof (see comments) for strings (theorems) in the MIU formal system that are n characters long.

1, 4, 13, 11, 18, 16, 25, 23, 24, 22, 26, 24, 34, 32, 33, 31, 35, 33, 34, 32, 39, 37, 49

Offset

2,2

Comments

See A368946 for the description of the MIU formal system, A369410 for the triangle of the corresponding proof lengths and A369409 for the definition of "normal" proof.

References

Douglas R. Hofstadter, Gödel, Escher, Bach: an Eternal Golden Braid, Basic Books, 1979, pp. 33-41.

Links

Table of n, a(n) for n=2..24.

Armando B. Matos and Luis Filipe Antunes, Short Proofs for MIU theorems, Technical Report Series DCC-98-01, University of Porto, 1998.

Wikipedia, MU Puzzle.

Index entries for sequences from "Goedel, Escher, Bach".

Formula

a(n) = max_{k=1..A024495(n)} A369410(n,k).

Mathematica

MIUDigitsW3[n_] := Select[Tuples[{0, 1}, n - 1], !Divisible[Count[#, 1], 3]&];
MIUProofLineCount[t_] := Module[{c = Count[t, 0], ni}, ni = Length[t] + 2*c; While[ni > 1, If[OddQ[ni], ni = (ni+3)/2; c += 4, ni/=2; c++]]; c+1];
Map[Max, Map[MIUProofLineCount, Array[MIUDigitsW3, 15, 2], {2}]]

Crossrefs

Cf. A024495, A368946, A369173, A369409, A369410, A369413.

Sequence in context: A160249 A173800 A175174 * A136137 A287895 A050223

Adjacent sequences: A369409 A369410 A369411 * A369413 A369414 A369415

Keyword

nonn,hard,more

Author

Paolo Xausa, Jan 23 2024

Status

approved