A332235 Least integer t such that every binary word of length t+1 contains an split occurrence of an n-overlap.

2, 4, 12, 47

Offset

0,1

Comments

An "n-overlap" is a word of the form xxx', where x is a nonempty word of length at least n, and x' is a prefix of x of length n. Thus, for example, abcdabcdab is a 2-overlap. A split occurrence of a pattern p is a word of the form xyz where xz matches the pattern.

For n = 0,1,2,3 the lexicographically least words achieving the bound are:

n = 0: 01

n = 1: 0011

n = 2: 000110100111

n = 3: 00111010100001010011101000011111000011010001110

Links

Table of n, a(n) for n=0..3.

D. Gabric and J. Shallit, Avoidance of split overlaps, arxiv preprint arXiv:2002.01968 [cs.DM], February 5 2020.

Crossrefs

Cf. A332234.

Sequence in context: A074449 A364622 A359328 * A131387 A207647 A152453

Adjacent sequences: A332232 A332233 A332234 * A332236 A332237 A332238

Keyword

nonn,more

Author

Jeffrey Shallit, Feb 07 2020

Status

approved