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A213971
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List of primitive words over the alphabet {2,3}.
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2
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2, 3, 23, 32, 223, 232, 233, 322, 323, 332, 2223, 2232, 2233, 2322, 2332, 2333, 3222, 3223, 3233, 3322, 3323, 3332, 22223, 22232, 22233, 22322, 22323, 22332, 22333, 23222, 23223, 23232, 23233, 23322, 23323, 23332, 23333, 32222, 32223, 32232, 32233, 32322, 32323, 32332, 32333, 33222, 33223, 33232, 33233, 33322, 33323, 33332
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OFFSET
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1,1
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COMMENTS
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A word w is primitive if it cannot be written as u^k with k>1; otherwise it is imprimitive.
The {0,1} version of this sequence is
0, 1, 01, 10, 001, 010, 011, 100, 101, 110, 0001, 0010, 0011, 0100, 0110, 0111, 1000, 1001, 1011, 1100, 1101, 1110, 00001, 00010, 00011, 00100, 00101, 00110, 00111, 01000, 01001, 01010, 01011, 01100, 01101, 01110, 01111, 10000, 10001, 10010, 10011, 10100, 10101, 10110, 10111, 11000, 11001, 11010, 11011, 11100, 11101, 11110, ...,
but this cannot be included as a sequence in the OEIS since it contains nonzero "numbers" beginning with 0.
The Lyndon words over {2,3} are the intersection of this sequence with A239016. - M. F. Hasler, Mar 10 2014
This sequence results from A213970 by replacing all digits 1 by 2, and from A213969 by replacing all digits 2 by 3 and digits 1 by 2. - M. F. Hasler, Mar 10 2014
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REFERENCES
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A. de Luca and S. Varricchio, Finiteness and Regularity in Semigroups and Formal Languages, Monographs in Theoretical Computer Science, Springer-Verlag, Berlin, 1999. See p. 10.
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LINKS
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FORMULA
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PROG
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(PARI) for(n=1, 5, p=vector(n, i, 10^(n-i))~; forvec(d=vector(n, i, [2, 3]), is_A239017(m=d*p)&&print1(m", "))) \\ M. F. Hasler, Mar 10 2014
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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