A360528 Numbers n for which the length-n prefix of the Fibonacci word (A003849) ends in a word of exponent >= (3+sqrt(5))/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

Table of n, a(n) for n=1..63.

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

Cf. A003849, A360531, A360532.

Sequence in context: A293817 A360097 A360258 * A336004 A296795 A079831

Adjacent sequences: A360525 A360526 A360527 * A360529 A360530 A360531

Keyword

nonn

Author

Jeffrey Shallit, Feb 10 2023

Status

approved