A213970 -id:A213970 - cp's OEIS frontend

A213974 List of imprimitive words over the alphabet {2,3}.

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

Offset: 1

N. J. A. Sloane, Jun 30 2012

nonn

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

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.

Cf. A213969, A213970, A213971, A213972, A213973.

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

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

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

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

Original entry on oeis.org

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

N. J. A. Sloane, Jun 30 2012

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

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.

Cf. A213969-A213974.

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

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

cp's OEIS Frontend

A213974 List of imprimitive words over the alphabet {2,3}.

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