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A213971
List of primitive words over the alphabet {2,3}.
2
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
OFFSET
1,1
COMMENTS
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
REFERENCES
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.
FORMULA
A213971 = A032810 intersect A239017. - M. F. Hasler, Mar 10 2014
PROG
(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
CROSSREFS
KEYWORD
nonn,base
AUTHOR
N. J. A. Sloane, Jun 30 2012
STATUS
approved