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A213974 List of imprimitive words over the alphabet {2,3}. 8
22, 33, 222, 333, 2222, 2323, 3232, 3333, 22222, 33333, 222222, 223223, 232232, 232323, 233233, 322322, 323232, 323323, 332332, 333333, 2222222, 3333333, 22222222, 22232223, 22322232, 22332233, 23222322, 23232323, 23322332, 23332333, 32223222, 32233223, 32323232, 32333233, 33223322, 33233323, 33323332, 33333333 (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 00, 11, 000, 111, 0000, 0101, 1010, 1111, 00000, 11111, 000000, 001001, 010010, 010101, 011011, 100100, 101010, 101101, 110110, 111111 but this cannot be included as a sequence in the OEIS since it contains nonzero "numbers" beginning with 0.

This sequence results from A213973 by replacing each digit 1 by 2, and from A213972 by replacing all digits 2 by 3 and all 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..38.

FORMULA

Equals A032810 intersect A239018. - M. F. Hasler, Mar 10 2014

PROG

(PARI) for(n=1, 8, 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, A213970, A213971, A213972, A213973.

Sequence in context: A095044 A020151 A071265 * A103320 A306882 A125526

Adjacent sequences:  A213971 A213972 A213973 * A213975 A213976 A213977

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Jun 30 2012

EXTENSIONS

More terms from M. F. Hasler, Mar 10 2014

STATUS

approved

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Last modified August 20 22:45 EDT 2019. Contains 326155 sequences. (Running on oeis4.)