# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a360528 Showing 1-1 of 1 %I A360528 #12 Feb 10 2023 12:55:18 %S A360528 13,14,22,23,24,26,27,34,35,36,37,38,39,40,43,44,45,47,48,56,57,58,59, %T A360528 60,61,62,63,64,65,66,68,69,70,71,72,73,74,77,78,79,81,82,89,90,91,92, %U A360528 93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,111 %N A360528 Numbers n for which the length-n prefix of the Fibonacci word (A003849) ends in a word of exponent >= (3+sqrt(5))/2. %C A360528 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. %C A360528 This sequence is the complement of the union of A360531, A360532, and the integer 1. %H A360528 F. Mignosi, A. Restivo, and S. Salemi, Periodicity and the golden ratio, Theor. Comput. Sci. 204 (1998), 153-167. %H A360528 Jeffrey Shallit, Prefixes of the Fibonacci word, Arxiv preprint arXiv:2302.04640 [cs.FL], February 9 2023. %e A360528 For n = 13 the prefix of length 13 is 0100101001001, which has the suffix 01001001 with exponent 8/3. %Y A360528 Cf. A003849, A360531, A360532. %K A360528 nonn %O A360528 1,1 %A A360528 _Jeffrey Shallit_, Feb 10 2023 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE