A213971 List of primitive words over the alphabet {2,3}.

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

Author

N. J. A. Sloane, Jun 30 2012

Keywords

• nonn
• base

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.

Crossrefs

Cf. A213969-A213974.

Programs

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

Formula

A213971 = A032810 intersect A239017. - M. F. Hasler, Mar 10 2014