A102660 List of Lyndon words on {1,2,3} sorted first by length and then lexicographically.

1, 2, 3, 12, 13, 23, 112, 113, 122, 123, 132, 133, 223, 233, 1112, 1113, 1122, 1123, 1132, 1133, 1213, 1222, 1223, 1232, 1233, 1322, 1323, 1332, 1333, 2223, 2233, 2333, 11112, 11113, 11122, 11123, 11132, 11133, 11212, 11213, 11222, 11223, 11232

Offset: 1

Author

N. J. A. Sloane, Feb 03 2005

Keywords

• nonn
• easy

Comments

A Lyndon word is primitive (not a power of another word) and is earlier in lexicographic order than any of its cyclic shifts.

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
• F. Bassino, J. Clement and C. Nicaud, The standard factorization of Lyndon words: an average point of view, Discrete Math. 290 (2005), 1-25.
• Reinhard Zumkeller, Haskell programs for some sequences concerning Lyndon words
• Wikipedia, Lyndon word
• Index entries for sequences related to Lyndon words

Crossrefs

Cf. A074650, A001037, A102659, A210584, A210585.

Cf. A027376.

Programs

Haskell

cf. link.

PARI

is_A102660(n)=is_A239016(n)&&is_A239017(n)
for(n=1, 5, p=vector(n, i, 10^(n-i))~; forvec(d=vector(n, i, [1, 3]), is_A102660(m=d*p)&&print1(m", "))) \\ M. F. Hasler, Mar 09 2014

Formula

Equals A239016 intersect A239017. - M. F. Hasler, Mar 09 2014

Extensions

More terms from John W. Layman, Jan 24 2006

Definition improved by Reinhard Zumkeller, Mar 23 2012