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 A213969 List of primitive words over the alphabet {1,2}. 11
 1, 2, 12, 21, 112, 121, 122, 211, 212, 221, 1112, 1121, 1122, 1211, 1221, 1222, 2111, 2112, 2122, 2211, 2212, 2221, 11112, 11121, 11122, 11211, 11212, 11221, 11222, 12111, 12112, 12121, 12122, 12211, 12212, 12221, 12222, 21111, 21112, 21121, 21122, 21211, 21212, 21221, 21222, 22111, 22112, 22121, 22122, 22211, 22212, 22221 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 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 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, ..., but this cannot be included as a sequence in the OEIS since it contains nonzero "numbers" beginning with 0. Lyndon words on {1,2}, A102659, are the numbers in this sequence which are also not larger than any of their rotations, i.e., in A239016. - M. F. Hasler, Mar 08 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 Robert Israel, Table of n, a(n) for n = 1..16222 (all terms with up to 13 digits) MAPLE P:= proc(d) local m, A;     A:= map(t -> (10^d-1)/9 + add(10^s, s = t), combinat:-powerset([\$0..d-1]));     for m in numtheory:-divisors(d) minus {d} do       A:= remove(t -> t = (t mod 10^m)*(10^d-1)/(10^m-1), A);     od;     op(sort(A)); end proc: seq(P(d), d=1..6); # Robert Israel, Mar 24 2017 MATHEMATICA j[w_, k_] := FromDigits /@ (Flatten[Table[#, {k}]] & /@ w); L[n_] := Complement[ FromDigits /@ Tuples[{1, 2}, n], Union[ Flatten[( j[Tuples[{1, 2}, #1], n/#1] &) /@ Most[ Divisors[n]]]]]; Flatten@ Array[L, 5] (* Giovanni Resta, Mar 24 2017 *) PROG (PARI) is_A213969(n)={fordiv(#n=digits(n), L, L<#n&&n==concat(Col(vector(#n/L, i, 1)~*vecextract(n, 2^L-1))~)&&return); !setminus(Set(n), [1, 2])} for(n=1, 5, p=vector(n, i, 10^(n-i))~; forvec(d=vector(n, i, [1, 2]), is_A213969(m=d*p)&&print1(m", "))) \\ M. F. Hasler, Mar 08 2014 CROSSREFS Cf. A213969-A213974. Sequence in context: A053890 A053896 A155890 * A199986 A336528 A077410 Adjacent sequences:  A213966 A213967 A213968 * A213970 A213971 A213972 KEYWORD nonn,base AUTHOR N. J. A. Sloane, Jun 30 2012 STATUS approved

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Last modified September 21 12:30 EDT 2020. Contains 337271 sequences. (Running on oeis4.)