A321252 (Conjecturally) the lexicographically earliest infinite sequence over {0,1,2,3} avoiding abelian squares.

0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 1, 0, 1, 3, 1, 0, 1, 2, 1, 3, 2, 0, 2, 1, 0, 1, 3, 0, 1, 0, 2, 0, 3, 0, 2, 0, 1, 2, 0, 2, 3, 1, 0, 1, 2, 0, 2, 3, 2, 0, 2, 1, 2, 3, 0, 3, 2, 3, 0, 1, 0, 2, 0, 3, 0, 2, 0, 1, 2, 1, 3, 0, 1, 0, 2, 0, 3, 0, 1, 3, 0, 3, 2

Offset

1,4

Comments

An abelian square is a nonempty string where the second half is a rearrangement of the first half, like the English word "reappear". To "avoid" an abelian square means to have no contiguous block of that form. Although an easy compactness argument, combined with a result of Keränen (1992) shows that the lexicographically earliest infinite string avoiding abelian squares over the alphabet {0,1,2,3} must exist, the terms provided are only conjecturally part of the described sequence, because we have no proof currently that this particular string can be extended infinitely far to the right.

Links

Table of n, a(n) for n=1..85.

Veikko Keränen, Abelian squares are avoidable on 4 letters, in ICALP 1992, volume 623 of Lecture Notes in Comput. Sci., pages 41-52. Springer-Verlag, 1992.

Crossrefs

Cf. A272653, A272654, A272655.

Sequence in context: A272216 A349906 A320439 * A225345 A335427 A083280

Adjacent sequences: A321249 A321250 A321251 * A321253 A321254 A321255

Keyword

nonn

Author

Jeffrey Shallit, Nov 01 2018

Status

approved