生成正常数字的不可思议的子序列选择
Uncanny subsequence selections that generate normal numbers
摘要：
给定一个实数$0.a_1a_2 a_3\dots$，它与基$b$正交，我们检查递增序列$n_i$，使得数$0.a_{n_1}a_{n_2}a_{n_3}\dots$与基$b$正交。经典上已知，如果$n_i$形成等差数列，则这将起作用。我们给出了更多的构造，包括基于数字$a_i$递归定义的$n_i$。特别感兴趣的是，我们表明，如果一个数字是正常的基础$b$，然后删除所有的数字从其扩展等于$(b-1)$离开基地- $(b-1)$扩展是正常的基础$(b-1)$。
英文摘要：
Given a real number $0.a_1a_2 a_3\dots$ that is normal to base $b$, we examine increasing sequences $n_i$ so that the number $0.a_{n_1}a_{n_2}a_{n_3}\dots$ are normal to base $b$. Classically it is known that if the $n_i$ form an arithmetic progression then this will work. We give several more constructions, including $n_i$ that are recursively defined based on the digits $a_i$. Of particular interest, we show that if a number is normal to base $b$, then removing all the digits from its expansion which equal $(b-1)$ leaves a base-$(b-1)$ expansion that is normal to base $(b-1)$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
