论文标题
关于连续数字与原始数量之间的差异
On differences between consecutive numbers coprime to primorials
论文作者
论文摘要
我们考虑到给定基础数字的次数有序序列，并研究连续元素之间的差异。 jacobsthal函数应用于基础，事实证明代表了这些差异中最大的函数。我们将探索最小的数字，而不会发生这种差异。关于雅各布斯特尔函数以下的自然数，几乎不知道，这不能表示为连续数字与基础的连续数之间的差异。这些数字的存在和频率尚未澄清。使用连续整数序列的限制覆盖范围与发生差异之间的关系，我们得出了一个界限，以下所有自然数都是连续数字之间的差异与给定的原始$ p_k \＃$之间的差异。此外，我们为普莱斯的不存在差异提供详尽的计算结果$ p_k $升至$ k = 44 $。数据表明，当$ h（n）$ $ h（n）$的范围差异是$ h（n）$的差异是$ h（n）$的差异，即$ h（k-1）$的所有自然数字是将jacobsthal函数应用于$ p_n \＃$。
We consider the ordered sequence of coprimes to a given primorial number and investigate differences between consecutive elements. The Jacobsthal function applied to the concerning primorial turns out to represent the greatest of these differences. We will explore the smallest even number which does not occur as such a difference. Little is known about even natural numbers below the respective Jacobsthal function which cannot be represented as a difference between consecutive numbers coprime to a primorial. Existence and frequency of these numbers have not yet been clarified. Using the relation between restricted coverings of sequences of consecutive integers and the occuring differences, we derive a bound below which all even natural numbers are differences between consecutive numbers coprime to a given primorial $p_k\#$. Furthermore, we provide exhaustive computational results on non-existent differences for primes $p_k$ up to $k=44$. The data suggest the assumption that all even natural numbers up to $h(k-1)$ occur as differences of coprimes to $p_k\#$ where $h(n)$ is the Jacobsthal function applied to $p_n\#$.
