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%I #10 Mar 10 2014 01:07:32
%S 11,33,111,333,1111,1313,3131,3333,11111,33333,111111,113113,131131,
%T 131313,133133,311311,313131,313313,331331,333333,1111111,3333333,
%U 11111111,11131113,11311131,11331133,13111311,13131313,13311331,13331333,31113111,31133113,31313131
%N List of imprimitive words over the alphabet {1,3}.
%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
%C 00, 11, 000, 111, 0000, 0101, 1010, 1111, 00000, 11111, 000000, 001001, 010010, 010101, 011011, 100100, 101010, 101101, 110110, 111111
%C but this cannot be included as a sequence in the OEIS since it contains nonzero "numbers" beginning with 0.
%C This sequence results from A213972 by replacing all digits 2 by 3, and from A213974 by replacing all digits 2 by 1. - _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 A213973 = A032917 intersect A239018. - _M. F. Hasler_, Mar 10 2014
%o (PARI) for(n=1, 8, p=2*vector(n, i, 10^(n-i))~; forvec(d=vector(n, i, [1, 3]/2), is_A239017(m=d*p)||print1(m", ")))
%Y Cf. A213969-A213974.
%K nonn,base
%O 1,1
%A _N. J. A. Sloane_, Jun 30 2012
%E More terms from _M. F. Hasler_, Mar 10 2014
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