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A360528
Numbers n for which the length-n prefix of the Fibonacci word (A003849) ends in a word of exponent >= (3+sqrt(5))/2.
2
13, 14, 22, 23, 24, 26, 27, 34, 35, 36, 37, 38, 39, 40, 43, 44, 45, 47, 48, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 68, 69, 70, 71, 72, 73, 74, 77, 78, 79, 81, 82, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 111
OFFSET
1,1
COMMENTS
A word w = w[1..n] has period p>=1 if w[i]=w[i+p] for 1 <= i <= n-p. The exponent of w is defined to be n/q, where q is the smallest period of w.
This sequence is the complement of the union of A360531, A360532, and the integer 1.
LINKS
F. Mignosi, A. Restivo, and S. Salemi, Periodicity and the golden ratio, Theor. Comput. Sci. 204 (1998), 153-167.
Jeffrey Shallit, Prefixes of the Fibonacci word, Arxiv preprint arXiv:2302.04640 [cs.FL], February 9 2023.
EXAMPLE
For n = 13 the prefix of length 13 is 0100101001001, which has the suffix 01001001 with exponent 8/3.
CROSSREFS
KEYWORD
nonn
AUTHOR
Jeffrey Shallit, Feb 10 2023
STATUS
approved