论文标题
决定因子霍索亚三角的素数和复合材料
Primes and composites in the determinant Hosoya triangle
论文作者
论文摘要
在本文中，我们查看$ h_ {r，k}形式的数字：= f_ {k-1} f_ {r-k+2}+f_ {k} f_ {k} f_ {r-k} $。这些数字是一个三角阵列的条目，称为\ emph {decialant hosoya triangle}，我们用$ {\ Mathcal h} $表示，该阵列表示该数组。我们讨论了上述数字及其原始性的划分属性。我们给出一小片序列，以说明$ {\ Mathcal H} $中的质数密度。由于斐波那契和卢卡斯的数字以$ {\ Mathcal H} $中的条目出现，因此我们的研究是关于是否有无限很多斐波那契或卢卡斯素数的经典问题的扩展。我们证明$ {\ Mathcal H} $具有任意的复合条目社区。最后，我们提供了大量的数据，表明$ {\ Mathcal H} $中的素数非常高。
In this paper, we look at numbers of the form $H_{r,k}:=F_{k-1}F_{r-k+2}+F_{k}F_{r-k}$. These numbers are the entries of a triangular array called the \emph{determinant Hosoya triangle} which we denote by ${\mathcal H}$. We discuss the divisibility properties of the above numbers and their primality. We give a small sieve of primes to illustrate the density of prime numbers in ${\mathcal H}$. Since the Fibonacci and Lucas numbers appear as entries in ${\mathcal H}$, our research is an extension of the classical questions concerning whether there are infinitely many Fibonacci or Lucas primes. We prove that ${\mathcal H}$ has arbitrarily large neighbourhoods of composite entries. Finally we present an abundance of data indicating a very high density of primes in ${\mathcal H}$.
