论文标题
Dyck数字，ii。 OEIS A036991中的三胞胎和根树
Dyck Numbers, II. Triplets and Rooted Trees in OEIS A036991
论文作者
论文摘要
Dyck路径是研究最广泛的加泰罗尼亚家庭之一。本文是[2]的延续。在本文中，我们正在处理戴克路径的编号，OEI序列A036991或戴克数的术语。我们考虑形式（T-4，T-2，T）的术语的三胞胎（T是高级任期）；三胞胎覆盖A036991的80％。三胞胎包括所有梅森（Mersenne）的数字，每个默森（Mersenne）的数字在某个三胞胎中都是高级任期。三元组分布在A036991范围内；范围的长度和范围内的三胞胎数量都按OEIS序列A001405的术语计数。除了三胞胎外，范围中还有许多孤独的术语，这些术语由OEIS序列A116385的术语计算。每个孤独的术语（其中有一个无限的数量）是无限三元树的根。结果，A036991序列是这样有针对性树的森林。我们在A036991的无限三元树上测试了双重猜想。我们考虑了一对质子数的无限定理，差异不超过4。
Dyck paths are among the most heavily studied Catalan families. This paper is a continuation of [2]. In the paper we are dealing with the numbering of Dyck paths, the terms of the OEIS sequence A036991 or Dyck numbers. We consider triplets of terms of the form (t-4, t-2, t) (t is the senior term); triplets cover 80% of A036991. Triplets include all Mersenne numbers, with each Mersenne number being a senior term in some triplet. Triples are distributed over A036991 ranges; both the length of the ranges and the number of triplets in the range are counted by the terms of the OEIS sequence A001405. In addition to triplets, there are many lone terms in the ranges, which are counted by the terms of the OEIS sequence A116385. Each lone term (there are an infinite number of them) is the root of an infinite ternary tree of triplets. As a result, the sequence A036991 is a forest of such directed trees. We test the twin prime conjecture on infinite ternary trees of A036991. We consider the infinity theorem for pairs of prime numbers that differ by no more than 4.
