论文标题
具有主要功率歧视器的二次序列
Quadratic sequences with prime power discriminators
论文作者
论文摘要
整数序列$ \ textbf {s} =（s（i））_ {i \ geq 0} $的区分器，由Arnold，Benkoski和McCabe在1985年介绍，是函数$ d _ {\ textbf {s}} $ d $ d $ d _ $ d _ d _ { s（1），\ ldots，s（n -1）$是成对的不一致的modulo $ m $。在本说明中，我们尝试确定所有二次序列，其歧视器由$ p^{\ lceil \ log_p n \ rceil} $用于prime $ p $，即$ p $的最小功率，即$ \ geq n $。我们确定$ P = 2 $的所有此类序列，表明$ P \ geq 5 $没有，并为$ P = 3 $提供一些部分结果。
The discriminator of an integer sequence $\textbf{s} = (s(i))_{i \geq 0}$, introduced by Arnold, Benkoski, and McCabe in 1985, is the function $D_{\textbf{s}} (n)$ that sends $n$ to the least integer $m$ such that the numbers $s(0), s(1), \ldots, s(n - 1)$ are pairwise incongruent modulo $m$. In this note, we try to determine all quadratic sequences whose discriminator is given by $p^{\lceil \log_p n \rceil}$ for prime $p$, i.e., the smallest power of $p$ which is $\geq n$. We determine all such sequences for $p = 2$, show that there are none for $p \geq 5$, and provide some partial results for $p = 3$.
