A213970 - OEIS

A213970

List of primitive words over the alphabet {1,3}.

1, 3, 13, 31, 113, 131, 133, 311, 313, 331, 1113, 1131, 1133, 1311, 1331, 1333, 3111, 3113, 3133, 3311, 3313, 3331, 11113, 11131, 11133, 11311, 11313, 11331, 11333, 13111, 13113, 13131, 13133, 13311, 13313, 13331, 13333, 31111, 31113, 31131, 31133, 31311, 31313, 31331, 31333, 33111, 33113, 33131, 33133, 33311, 33313, 33331

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OFFSET

1,2

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.

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.

CROSSREFS

Cf. A213969-A213974.

Sequence in context: A146191 A058264 A242905 * A034050 A107689 A339945

Adjacent sequences: A213967 A213968 A213969 * A213971 A213972 A213973

KEYWORD

nonn,base

AUTHOR

N. J. A. Sloane, Jun 30 2012

STATUS

approved