

A329318


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


20



1, 2, 21, 211, 221, 2111, 2211, 2221, 21111, 21211, 22111, 22121, 22211, 22221, 211111, 212111, 221111, 221121, 221211, 222111, 222121, 222211, 222221, 2111111, 2112111, 2121111, 2121211, 2211111, 2211121, 2211211, 2212111, 2212121, 2212211, 2221111, 2221121
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OFFSET

1,2


COMMENTS

The coLyndon product of two or more finite sequences is defined to be the lexicographically minimal sequence obtainable by shuffling the sequences together. For example, the coLyndon product of (231) and (213) is (212313), the product of (221) and (213) is (212213), and the product of (122) and (2121) is (1212122). A coLyndon word is a finite sequence that is prime with respect to the coLyndon product. Equivalently, a coLyndon word is a finite sequence that is lexicographically strictly greater than all of its cyclic rotations. Every finite sequence has a unique (orderless) factorization into coLyndon words, and if these factors are arranged in a certain order, their concatenation is equal to their coLyndon product. For example, (1001) has sorted coLyndon factorization (1)(100).


LINKS

Table of n, a(n) for n=1..35.


MATHEMATICA

colynQ[q_]:=Array[Union[{RotateRight[q, #], q}]=={RotateRight[q, #], q}&, Length[q]1, 1, And];
Join@@Table[FromDigits/@Select[Tuples[{1, 2}, n], colynQ], {n, 5}]


CROSSREFS

The non"co" version is A102659.
Numbers whose binary expansion is coLyndon are A275692.
Length of the coLyndon factorization of the binary expansion is A329312.
Cf. A000031, A001037, A027375, A059966, A060223, A211100, A328596, A329324.
Sequence in context: A131584 A037736 A328073 * A037559 A042349 A037495
Adjacent sequences: A329315 A329316 A329317 * A329319 A329320 A329321


KEYWORD

nonn


AUTHOR

Gus Wiseman, Nov 11 2019


STATUS

approved



