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A369172
Irregular triangle read by rows: row n lists the lengths of the strings of the MIU formal system at the n-th level of the tree generated by recursively applying the system rules, starting from the MI string.
4
2, 3, 3, 5, 4, 5, 9, 7, 6, 9, 3, 3, 17, 13, 11, 4, 4, 10, 17, 7, 7, 7, 7, 7, 7, 4, 5, 5, 33, 25, 21, 9, 9, 9, 9, 7, 7, 2, 19, 8, 8, 8, 8, 8, 8, 18, 33, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 8, 13, 5, 5, 5, 8, 13, 5, 5, 8, 13, 5, 8, 13, 5, 8, 13, 5, 5, 13, 5, 5, 5, 7, 6, 9, 9
OFFSET
0,1
COMMENTS
See A368946 for the description of the MIU formal system and the triangle of corresponding strings.
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 = 0..3670 (rows 0..7 of the triangle, flattened).
Wikipedia, MU Puzzle.
FORMULA
T(n,k) = A055642(A368946(n,k)).
T(n,k) = A369206(n,k) + A369207(n,k) + 1.
EXAMPLE
Triangle begins:
[0] 2;
[1] 3 3;
[2] 5 4 5;
[3] 9 7 6 9 3 3;
[4] 17 13 11 4 4 10 17 7 7 7 7 7 7 4 5 5;
...
MATHEMATICA
MIUStepOW3[s_] := Flatten[Map[{If[StringEndsQ[#, "1"], # <> "0", Nothing], # <> #, StringReplaceList[#, "111" -> "0"], StringReplaceList[#, "00" -> ""]}&, s]];
With[{rowmax = 5}, StringLength[NestList[MIUStepOW3, {"1"}, rowmax]]] + 1
CROSSREFS
Cf. A055642, A368946, A368947 (row lengths), A369206, A369207.
Sequence in context: A086898 A123031 A271709 * A373815 A359042 A159070
KEYWORD
nonn,tabf
AUTHOR
Paolo Xausa, Jan 15 2024
STATUS
approved