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A213973
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List of imprimitive words over the alphabet {1,3}.
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5
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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)
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OFFSET
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1,1
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COMMENTS
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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
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REFERENCES
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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.
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LINKS
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Table of n, a(n) for n=1..33.
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FORMULA
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A213973 = A032917 intersect A239018. - M. F. Hasler, Mar 10 2014
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PROG
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(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", ")))
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CROSSREFS
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Cf. A213969-A213974.
Sequence in context: A120354 A206527 A297478 * A262913 A179204 A328606
Adjacent sequences: A213970 A213971 A213972 * A213974 A213975 A213976
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KEYWORD
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nonn,base
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AUTHOR
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N. J. A. Sloane, Jun 30 2012
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EXTENSIONS
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More terms from M. F. Hasler, Mar 10 2014
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STATUS
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approved
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