A239017 List of primitive words on {1,2,3}.

1, 2, 3, 12, 13, 21, 23, 31, 32, 112, 113, 121, 122, 123, 131, 132, 133, 211, 212, 213, 221, 223, 231, 232, 233, 311, 312, 313, 321, 322, 323, 331, 332, 1112, 1113, 1121, 1122, 1123, 1131, 1132, 1133, 1211, 1213, 1221, 1222, 1223, 1231, 1232, 1233, 1311, 1312, 1321, 1322, 1323, 1331, 1332, 1333, 2111, 2112, 2113, 2122, 2123

Offset

1,2

Comments

A word is primitive if it is not a power (i.e., repetition) of a subword. The non-primitive words 11, 22, 33, 111, 222, 333, 1111, 1212, 1313, 2121, 2222, ... (cf. A239018) are excluded here.

This sequence is the complement of A239018 in A007932.

It is the analog for {1,2,3} of A213969 for {1,2}.

The Lyndon words on {1,2,3}, A102660, are the subsequence of these primitive words not larger than any of their "rotations", i.e., in A239016.

Links

Table of n, a(n) for n=1..62.

Formula

A239017 = A007932 \ A239018.

Prog

(PARI) is_A239017(n)={fordiv(#d=digits(n), L, L<#d&&d==concat(Col(vector(#d/L, i, 1)~*vecextract(d, 2^L-1))~)&&return); !setminus(Set(d), [1, 2, 3])}
for(n=1, 5, p=vector(n, i, 10^(n-i))~; forvec(d=vector(n, i, [1, 3]), is_A239017(m=d*p)&&print1(m", ")))

Crossrefs

Cf. A213969 - A213974.

Sequence in context: A255567 A039565 A032805 * A157899 A157900 A157902

Adjacent sequences: A239014 A239015 A239016 * A239018 A239019 A239020

Keyword

nonn,base

Author

M. F. Hasler, Mar 08 2014

Status

approved