关于三角形数补数及其渐近性质

On the triangle Number's Complement and its Asymptotic Properties

对任意正整数n,设a(n)表示n的三角形数补数,即就是a(n)是最小的非负整数使得n+a(n)为一三角形数m(m+1)2.用初等和解析的方法研究了三角形数补数列狖a(n)狚(n=1,2,3,···)的渐近性质,给出了两种不同类型的渐近公式.

For any positive integer n,let a(n)denotes the triangle number's complement.That is,for any fixed positive integer n,a(n) is the smallest nonnegative integer number such that n+a(n) be a triangel number ■.Using the elementary and analytic methods,it is to study the asymptotic properties of the triangle number complement sequence,and two interesting asymptotic formulas for it are obtained.