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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

Table of n, a(n) for n=1..33.

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.)