| 一类数论函数的迭代性质研究 |
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| 引用本文： | 任莹,李为东.一类数论函数的迭代性质研究[J].河南师范大学学报(自然科学版),2009,37(2). |
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| 作者姓名： | 任莹 李为东 |
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| 作者单位： | 北京科技大学,数力系,北京,100083 |
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| 基金项目： | 国家自然科学基金，北京科技大学校科研基金 |
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| 摘 要： | 首先对自然数引进了按照各位数字进行划分的分类方法,进而讨论了一类数论函数在这种分类方法之下的若干性质.研究了广义H-数高度以及与之相关的一些问题.在基底为2的情况下,各个高度的最小数恰好由数列M1=1,Mn+1=2Mn-1,n 1组成;高度为2的数的密度是零.在一般基底之下,给出计算各个高度的最小数的算法.
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| 关 键 词： | 数论函数 广义H-数 高度 m次迭代 Mersenne素数 |
Iteration Properties of Some Arithmetic Functions |
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| REN Ying,LI Wei-dong.Iteration Properties of Some Arithmetic Functions[J].Journal of Henan Normal University(Natural Science),2009,37(2). |
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| Authors: | REN Ying LI Wei-dong |
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| Institution: | Department of Mathematics and Mechanics;University of Science and Technology of Beijing;Beijing 100083;China |
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| Abstract: | In this paper,the new classification of positive number by its digits is introduced.Some properties of an arithmetic functions definied by digits of positive numbers have been concerned.The results of the height of generalized happy number and relative problems are given.When the base is two,the least numbers of each height consist of the sequence,and the density of height two is zero.On general base,the method of calculating the least numbers of each height has given. |
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| Keywords: | arithmetic function generalized happy number height mth iteration Mersenne prime |
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