cp's OEIS Frontend

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

%I A213971 #11 Mar 10 2014 01:15:30
%S A213971 2,3,23,32,223,232,233,322,323,332,2223,2232,2233,2322,2332,2333,3222,
%T A213971 3223,3233,3322,3323,3332,22223,22232,22233,22322,22323,22332,22333,
%U A213971 23222,23223,23232,23233,23322,23323,23332,23333,32222,32223,32232,32233,32322,32323,32332,32333,33222,33223,33232,33233,33322,33323,33332
%N A213971 List of primitive words over the alphabet {2,3}.
%C A213971 A word w is primitive if it cannot be written as u^k with k>1; otherwise it is imprimitive.
%C A213971 The {0,1} version of this sequence is
%C A213971 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, ...,
%C A213971 but this cannot be included as a sequence in the OEIS since it contains nonzero "numbers" beginning with 0.
%C A213971 The Lyndon words over {2,3} are the intersection of this sequence with A239016. - _M. F. Hasler_, Mar 10 2014
%C A213971 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
%D A213971 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 A213971 A213971 = A032810 intersect A239017. - _M. F. Hasler_, Mar 10 2014
%o A213971 (PARI) 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
%Y A213971 Cf. A213969-A213974.
%K A213971 nonn,base
%O A213971 1,1
%A A213971 _N. J. A. Sloane_, Jun 30 2012