OFFSET
0,3
COMMENTS
This value of k is chosen so that Z_k is the largest Zimin word that the binary expansion of n does not avoid.
LINKS
Peter Kagey, Table of n, a(n) for n = 0..8191
Peter Kagey, Matching ABACABA-type patterns, Code Golf Stack Exchange.
Danny Rorabaugh, Toward the Combinatorial Limit Theory of Free Words, arXiv preprint arXiv:1509.04372 [math.CO], 2015.
Wikipedia, Sesquipower.
EXAMPLE
For n = 121, the binary expansion is "1111001", which avoids the Zimin word Z_3 = ABACABA, but does not avoid the Zimin word Z_2 = ABA. In particular, there are a(121) = 7 substrings that are instances of Z_2:
(111)1001 with A = 1 and B = 1,
1(111)001 with A = 1 and B = 1,
(1111)001 with A = 1 and B = 11,
111(1001) with A = 1 and B = 00,
11(11001) with A = 1 and B = 100,
1(111001) with A = 1 and B = 1100, and
(1111001) with A = 1 and B = 11100.
CROSSREFS
KEYWORD
AUTHOR
Peter Kagey, Mar 14 2021
STATUS
approved