The main subject of this paper are binary pattern sequences, that is, sequences of the form ${(-1)}^{\mathrm{\#}(n,A)}$ where A is a set of strings of 0s and 1s, and $\mathrm{\#}(n,A)$ denotes the total number of times patterns from A appear in the binary expansion of n. A sequence is said to be noncorrelated if the corresponding spectral measure is equal to the Lebesgue measure.

We show that it is possible to algorithmically verify if a given binary pattern sequence is noncorrelated. As an application, we compute that there are exactly 2272 noncorrelated binary pattern sequences of length ≤4. If we restrict our attention to patterns that do not end with 0, we put forward a sufficient condition for a pattern sequence to be noncorrelated. We conjecture that this condition is also necessary, and verify this conjecture for lengths ≤5.

本文的主要主题是二进制模式序列，即形式为 ${（-\mathrm{1个}）}^{\mathrm{＃}（ñ，\mathrm{一种}）}$其中A是一组0 s和1 s的字符串，并且$\mathrm{＃}（ñ，\mathrm{一种}）$表示来自A的模式出现在n的二进制展开中的总次数。如果相应的频谱量度等于Lebesgue量度，则序列是不相关的。

我们表明，可以通过算法验证给定的二进制模式序列是否不相关。作为应用，我们计算出长度为≤4的正好有2272个不相关的二进制模式序列。如果我们将注意力集中在不以0结尾的模式上，则为模式序列不相关提出了充分的条件。我们推测此条件也是必要的，并验证长度≤5的该推测。