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A369172
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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.
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4
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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
(list;
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refs;
listen;
history;
text;
internal format)
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OFFSET
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0,1
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COMMENTS
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See A368946 for the description of the MIU formal system and the triangle of corresponding strings.
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REFERENCES
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Douglas R. Hofstadter, Gödel, Escher, Bach: an Eternal Golden Braid, Basic Books, 1979, pp. 33-41 and pp. 261-262.
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LINKS
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FORMULA
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EXAMPLE
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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;
...
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MATHEMATICA
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MIUStepOW3[s_] := Flatten[Map[{If[StringEndsQ[#, "1"], # <> "0", Nothing], # <> #, StringReplaceList[#, "111" -> "0"], StringReplaceList[#, "00" -> ""]}&, s]];
With[{rowmax = 5}, StringLength[NestList[MIUStepOW3, {"1"}, rowmax]]] + 1
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CROSSREFS
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KEYWORD
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nonn,tabf
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AUTHOR
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STATUS
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approved
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