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A278554 Number of distinct blocks of length n (aka subword complexity) of the characteristic sequence of the squarefree numbers A008966. 0
1, 2, 4, 8, 15, 29, 55, 101, 175, 323, 583 (list; graph; refs; listen; history; text; internal format)



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.


Table of n, a(n) for n=0..10.


For n = 5, the 3 blocks of length 5 that do not occur are 11111, 11110, and 01111.


Cf. A008966, A020754.

Sequence in context: A001383 A217733 A208976 * A335473 A224959 A108564

Adjacent sequences:  A278551 A278552 A278553 * A278555 A278556 A278557




Jeffrey Shallit, Jan 02 2017



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Last modified December 2 14:43 EST 2021. Contains 349445 sequences. (Running on oeis4.)