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 A213973 List of imprimitive words over the alphabet {1,3}. 5
 11, 33, 111, 333, 1111, 1313, 3131, 3333, 11111, 33333, 111111, 113113, 131131, 131313, 133133, 311311, 313131, 313313, 331331, 333333, 1111111, 3333333, 11111111, 11131113, 11311131, 11331133, 13111311, 13131313, 13311331, 13331333, 31113111, 31133113, 31313131 (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 A213972 by replacing all digits 2 by 3, and from A213974 by replacing all digits 2 by 1. - 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 A213973 = A032917 intersect A239018. - M. F. Hasler, Mar 10 2014 PROG (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", "))) CROSSREFS Cf. A213969-A213974. Sequence in context: A120354 A206527 A297478 * A262913 A179204 A328606 Adjacent sequences:  A213970 A213971 A213972 * A213974 A213975 A213976 KEYWORD nonn,base 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 August 19 18:30 EDT 2022. Contains 356229 sequences. (Running on oeis4.)