论文标题
全回旋和反植物粒细胞的商
Quotients of Palindromic and Antipalindromic Numbers
论文作者
论文摘要
如果其二进制代表读取相同的前向和向后读取，则据说自然的数字n是withindromic。在本文中，我们研究了两个全文数字的商，并回答了有关由此产生的整数和理性数字集的一些基本问题。例如，我们表明以下问题是算法可决定的：给定整数n，确定我们是否可以为palindromic数字a和B编写n = a/b。鉴于n是可表示的，我们找到了最小表示的分子大小的界限。我们证明，一组不代表性的整数在N中具有正密度。我们还获得了抗致分析数的商的相似结果（二进制表示的前半部分是下半部分的相反补充）。我们还提供示例，数值数据以及许多有趣的猜想和开放问题。
A natural number N is said to be palindromic if its binary representation reads the same forwards and backwards. In this paper we study the quotients of two palindromic numbers and answer some basic questions about the resulting sets of integers and rational numbers. For example, we show that the following problem is algorithmically decidable: given an integer N, determine if we can write N = A/B for palindromic numbers A and B. Given that N is representable, we find a bound on the size of the numerator of the smallest representation. We prove that the set of unrepresentable integers has positive density in N. We also obtain similar results for quotients of antipalindromic numbers (those for which the first half of the binary representation is the reverse complement of the second half). We also provide examples, numerical data, and a number of intriguing conjectures and open problems.
