A213974 - OEIS

%I #14 Aug 02 2017 12:01:25

%S 22,33,222,333,2222,2323,3232,3333,22222,33333,222222,223223,232232,

%T 232323,233233,322322,323232,323323,332332,333333,2222222,3333333,

%U 22222222,22232223,22322232,22332233,23222322,23232323,23322332,23332333,32223222,32233223,32323232,32333233,33223322,33233323,33323332,33333333

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

%C A word w is primitive if it cannot be written as u^k with k>1; otherwise it is imprimitive.

%C 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.

%C 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

%D 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.

%F Equals A032810 intersect A239018. - _M. F. Hasler_, Mar 10 2014

%o (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

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

%K nonn

%O 1,1

%A _N. J. A. Sloane_, Jun 30 2012

%E More terms from _M. F. Hasler_, Mar 10 2014