论文标题
斐波那契序列是正常的碱基10
The Fibonacci Sequence is Normal Base 10
论文作者
论文摘要
在本文中，我们表明fibonacci序列的串联为\ textit {normal} base $ 10 $，这意味着给定长度（$ k $）的每个字符串都与其他所有长度$ k $的字符串一样频繁发生（$ 1 $ $ k $（$ 2 $ $ 2 $），$ 2 $'s和许多$ 704 $'s和$ 808 $ 808 $'s）。尽管我们知道几乎每个数字都是正常的，但我们可以说很少。目前尚不清楚$ e $，$π$还是$ \ sqrt {2} $是正常的。我们表明，小数点背后的斐波那契序列会在$ 5^x \ times2^y $的每个底部创建一个正常的数字。然后，我们提供了可能将结果扩展到所有整数基础的证据，并声称斐波那契串联是\ textit {绝对正常}。
In this paper, we show that the concatenation of the Fibonacci sequence is \textit{normal} in base $10$, meaning every string of a given length, $k$, occurs as frequently as every other string of length $k$ (there are as many $1$'s as $2$'s and as many $704$'s and $808$'s). Although we know that almost every number is normal, we can name very few of them. It is still unclear if $e$, $π$, or $\sqrt{2}$ are normal. We show that concatenating the Fibonacci sequence behind a decimal creates a normal number in every base of the form $5^x\times2^y$. We then provide evidence that potentially extends our result to all integer bases, and claim that the Fibonacci concatenation is \textit{absolutely normal}.
