摘要
本文对Collatz问题中同高连续数的密度分布和长度进行了研究,精确地计算出了区间[1,2^(24))内属于同高连续数的整数个数.研究发现,区间[1,2~N)内同高连续数的密度随N的增大而增大;纠正了Garner的推断和预测;找出了[1,2^(30))内最长的同高连续数;并提出了两个猜想.
The density distribution and length of consecutive numbers of the sam?height in the Collatz problem are studied. The number of integers, K, which belong to n-tuples (n≥2) in interval [1,2N) (N= 1,2,...,24) is accurately calculated. It is found that the density d(2N) (=K/(2N-1) of K in [1,2N) is increased with N. This is a correction of Garner's inferences and prejudg-ments. The longest tuple in [1,230), which is the 176-tuple with initial number 722 067 240 has been found. In addition, two conjectures are proposed.
出处
《华中理工大学学报》
CSCD
北大核心
1992年第5期171-174,共4页
Journal of Huazhong University of Science and Technology
关键词
数论
Collatz
同高连续数
number theory
the Collatz problem
the 3x + 1 conjecture
the consecutive numbers of the same height
w-tuple
