论文标题
Prime-Power地图
The Prime-Power Map
论文作者
论文摘要
我们介绍了Pillai的Prime Map：Prime-Power地图的修改。该地图修理了$ 1 $，如果它是Prime-Power $ P^K $，则将其参数除以$ P $，否则从其参数中减去最大的Prime-Proper不超过它。我们研究了该地图对正整数的迭代，首先是与素图所知的迭代相似的结果。随后，我们将其动力学属性与地图的更易于管理的变体进行了比较，任何轨道都允许明确描述。最后，我们提出了一些实验观察结果，基于我们猜测，几乎每个轨道映射的每个轨道都不包含Prime Power。
We introduce a modification of Pillai's prime map: the prime-power map. This map fixes $1$, divides its argument by $p$ if it is a prime-power $p^k$, otherwise subtracts from its argument the largest prime-power not exceeding it. We study the iteration of this map over the positive integers, developing, firstly, results parallel to those known for the prime map. Subsequently, we compare its dynamical properties to those of a more manageable variant of the map under which any orbit admits an explicit description. Finally, we present some experimental observations, based on which we conjecture that almost every orbit of the prime-power map contains no prime-power.
