关于正整数的多角形数加法补数

On the complement of the polygonal number of positive integer

对于n∈N+,设a(n)表示n的多角形数加法补数部分,即a(n)是使n+a(n)为一多角形数(1/2)(2m+(r-2)m(m-1)),m∈N的最小的非负整数.运用初等方法研究了多角形数加法补数级数的敛散性以及均值性质,给出它的渐近公式.

For arbitary n∈N＋,let a（n） denotes the polygonal number additive complement.That is to say,for any fixed positive integern,a（n） is the smallest nonnegative integer number such that n＋a（n） is a polygonal number（1/2）（2m＋（r-2）m（m-1））.In this paper,the convergent property and asymptotic property of the polygonal number additive complement sequence are studied using the elementary method,and an asymptotic formula is obtained.