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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
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
Sequence in context: A095044 A020151 A071265 * A103320 A306882 A125526
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 April 23 10:29 EDT 2024. Contains 371905 sequences. (Running on oeis4.)