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%I #30 Dec 26 2021 23:34:25
%S 1,2,4,8,15,29,55,101,175,323,583
%N Number of distinct blocks of length n (a.k.a. subword complexity) of the characteristic sequence of the squarefree numbers A008966.
%C Conjecture 1: this is the number of binary sequences S of length n such that, for all primes p such that p^2 <= n, at least one of the p^2 linearly indexed subsequences of S with gap p^2 starting at the 1st, 2nd, ..., p^2-th position of S, is the all-zeros sequence. In other words, every block that is not explicitly ruled out by congruence conditions for the primes p with p^2 <= n should occur.
%C Conjecture 2: the last new block to actually occur is always 0^n (n copies of 0). Cf. A020754.
%e For n = 5, the 3 blocks of length 5 that do not occur are 11111, 11110, and 01111.
%Y Cf. A008966, A020754.
%K nonn,more
%O 0,2
%A _Jeffrey Shallit_, Jan 02 2017
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