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A369173
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Irregular triangle read by rows: row n lists all of the distinct derivable strings in the MIU formal system that are n characters long.
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15
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31, 301, 310, 311, 3001, 3010, 3011, 3100, 3101, 3110, 30001, 30010, 30011, 30100, 30101, 30110, 31000, 31001, 31010, 31100, 31111, 300001, 300010, 300011, 300100, 300101, 300110, 301000, 301001, 301010, 301100, 301111, 310000, 310001, 310010, 310100, 310111, 311000, 311011, 311101, 311110, 311111
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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2,1
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COMMENTS
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See A368946 for the description of the MIU formal system.
A string S can be derived in the MIU formal system if and only if S contains just one M (as its first character) and an arbitrary number of I and U characters, where the number of I characters is not divisible by 3 (see Wikipedia link).
Strings are encoded using the map M -> 3, I -> 1 and U -> 0, and then sorted.
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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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EXAMPLE
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Triangle begins:
[2] 31;
[3] 301 310 311;
[4] 3001 3010 3011 3100 3101 3110;
[5] 30001 30010 30011 30100 30101 30110 31000 31001 31010 31100 31111;
...
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MATHEMATICA
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A369173row[n_] := Map[FromDigits[Join[{3}, #]]&, Select[Tuples[{0, 1}, n - 1], !Divisible[Count[#, 1], 3]&]]; Array[A369173row, 5, 2]
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CROSSREFS
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Cf. A369586 (shortest proofs), A369408 (length of shortest proofs), A369587 (number of symbols of shortest proofs).
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KEYWORD
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nonn,tabf,easy
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AUTHOR
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STATUS
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approved
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