login
A239017
List of primitive words on {1,2,3}.
4
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.
FORMULA
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
Sequence in context: A255567 A039565 A032805 * A157899 A157900 A157902
KEYWORD
nonn,base
AUTHOR
M. F. Hasler, Mar 08 2014
STATUS
approved