论文标题
在Zeckendorf相关分区上使用Lucas序列
On Zeckendorf Related Partitions Using the Lucas Sequence
论文作者
论文摘要
Zeckendorf证明，每个正整数都具有独特的分区，作为非连续的斐波那契数。同样，每个自然数字都可以分为卢卡斯序列的非连续术语的总和，尽管这些分区不必是唯一的。在本文中，我们证明自然数在卢卡斯序列中最多可以具有两个不同的非连续分区，在分区中找到所有带有固定项的正整数，并计算自然数的比例的限制值，而自然数的比例并非唯一地分配到LUCAS序列中的非连续项之和。
Zeckendorf proved that every positive integer has a unique partition as a sum of non-consecutive Fibonacci numbers. Similarly, every natural number can be partitioned into a sum of non-consecutive terms of the Lucas sequence, although such partitions need not be unique. In this paper, we prove that a natural number can have at most two distinct non-consecutive partitions in the Lucas sequence, find all positive integers with a fixed term in their partition, and calculate the limiting value of the proportion of natural numbers that are not uniquely partitioned into the sum of non-consecutive terms in the Lucas sequence.
