Algorithmic classification of noncorrelated binary pattern sequences

The main subject of this paper are binary pattern sequences, that is, sequences the form (−1)#(n,A) where A is a set strings 0s and 1s, #(n,A) denotes total number times patterns from appear in expansion n. sequence said to be noncorrelated if corresponding spectral measure equal Lebesgue measure. We show it possible algorithmically verify given noncorrelated. As an application, we compute there exactly 2272 length ≤4. If restrict our attention do not end with 0, put forward sufficient condition for conjecture also necessary, lengths ≤5.