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A278554
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Number of distinct blocks of length n (a.k.a. subword complexity) of the characteristic sequence of the squarefree numbers A008966.
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0
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1, 2, 4, 8, 15, 29, 55, 101, 175, 323, 583
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OFFSET
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0,2
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COMMENTS
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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.
Conjecture 2: the last new block to actually occur is always 0^n (n copies of 0). Cf. A020754.
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LINKS
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EXAMPLE
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For n = 5, the 3 blocks of length 5 that do not occur are 11111, 11110, and 01111.
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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STATUS
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approved
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