%I #12 Feb 10 2023 12:55:18

%S 13,14,22,23,24,26,27,34,35,36,37,38,39,40,43,44,45,47,48,56,57,58,59,

%T 60,61,62,63,64,65,66,68,69,70,71,72,73,74,77,78,79,81,82,89,90,91,92,

%U 93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,111

%N Numbers n for which the length-n prefix of the Fibonacci word (A003849) ends in a word of exponent >= (3+sqrt(5))/2.

%C 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 This sequence is the complement of the union of A360531, A360532, and the integer 1.

%H F. Mignosi, A. Restivo, and S. Salemi, <a href="https://doi.org/10.1016/S0304-3975(98)00037-1">Periodicity and the golden ratio</a>, Theor. Comput. Sci. 204 (1998), 153-167.

%H Jeffrey Shallit, <a href="https://arxiv.org/abs/2302.04640">Prefixes of the Fibonacci word</a>, Arxiv preprint arXiv:2302.04640 [cs.FL], February 9 2023.

%e For n = 13 the prefix of length 13 is 0100101001001, which has the suffix 01001001 with exponent 8/3.

%Y Cf. A003849, A360531, A360532.

%K nonn

%O 1,1

%A _Jeffrey Shallit_, Feb 10 2023