Smarandache kn数字数列及其一类均值性质

The Smarandache kn-digital sequence and its mean value properties

k∈N+,1<k≤9,数列{a(k,n)}称作Smarandache kn数字数列,如果该数列中的每一个数都可以分成两部分,那么第二部分是第一部分的k倍.例如3n数字数列{a(3,n)}定义为{13,26,39,412,515,618,721,824,…}.利用初等及组合方法研究Smarandache kn数字数列的一类均值性质,并给出几个有趣的渐近公式.

For any positive integer 1k≤9,the sequences {a（k,n）} is called the Smarandache kn-digital sequence,if the digital of a（k,n） can be partitioned into two groups such that the second is k times bigger than the first.For example,{a（3,n）}={13,26,39,412,515,…} is called the Smarandache 3n-digital sequence.One kind mean value of the Smarandache kn-digital sequence is studied by the elementary and combinational method,and severel interesting asymptotic formulas are given.