OFFSET
2,2
COMMENTS
REFERENCES
Douglas R. Hofstadter, Gödel, Escher, Bach: an Eternal Golden Braid, Basic Books, 1979, pp. 33-41 and pp. 261-262.
LINKS
Paolo Xausa, Table of n, a(n) for n = 2..10922 (rows 2..14 of the triangle, flattened).
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.
FORMULA
EXAMPLE
Triangle begins:
[2] 1;
[3] 4 4 2;
[4] 13 13 8 13 8 8;
[5] 11 11 6 11 6 6 11 6 6 6 3;
...
For the theorem MIU (310), which is given by A369173(3,2), the "normal" proof is MI (31) -> MII (311) -> MIIII (31111) -> MIU (310), which consists of 4 lines: T(3,2) is therefore 4.
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[MIUProofLineCount, Array[MIUDigitsW3, 7, 2], {2}]
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Paolo Xausa, Jan 23 2024
STATUS
approved