论文标题
Gijswijt序列的增长率
The Growth Rate of Gijswijt's Sequence
论文作者
论文摘要
Gijswijt的序列几乎完全由小型整数组成。但是，众所周知，每个正整数最终都出现在序列中。在本文中，我们确定其增长率。 Specifically, we prove that for $n=4,5,6,\dots$, the number $n$ occurs for the first time at position $2\uparrow (2\uparrow(3\uparrow(4\uparrow(5\uparrow\cdots\uparrow((n-2)\uparrow α)))))$, where $\uparrow$ denotes exponentiation, and $α\ in（n-2，n-1）$是一个实数。我们的结果证实了Van de Bult等人猜想的增长率。
Gijswijt's sequence consists almost entirely of small positive integers. However, it is known that every positive integer eventually appears in the sequence. In this paper we determine its growth rate. Specifically, we prove that for $n=4,5,6,\dots$, the number $n$ occurs for the first time at position $2\uparrow (2\uparrow(3\uparrow(4\uparrow(5\uparrow\cdots\uparrow((n-2)\uparrow α)))))$, where $\uparrow$ denotes exponentiation, and $α\in(n-2,n-1)$ is a real number. Our result confirms the growth rate conjectured by van de Bult et al.
