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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 (list; graph; refs; listen; history; text; internal format)
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.

LINKS

Table of n, a(n) for n=1..52.

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

Cf. A213969-A213974.

Sequence in context: A220569 A328940 A024764 * A024773 A176892 A109615

Adjacent sequences:  A213968 A213969 A213970 * A213972 A213973 A213974

KEYWORD

nonn,base

AUTHOR

N. J. A. Sloane, Jun 30 2012

STATUS

approved

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Last modified September 20 14:17 EDT 2020. Contains 337264 sequences. (Running on oeis4.)