In this paper, a sequence{Xn} is considered. It satisfies the equationXn = Yn(mod 2) in which Yn∈Z+, Y0≥2, Yn+1 = Yn + [Yn/2]. It is proved that the sequence{Xn} is an independent random variables sequence and a time homogeneous Markov chain. Based on the properties of the Markov chain{X n} , it is demonstrated that any edge of the initial circle C m is interpolated at least one new node after finite steps of circular interpolation.%研究序列{Xn},{Xn}满足Xn = Yn(mod 2),其中Yn∈Z+, Y0≥2, Yn+1= Yn +[Yn/2],证明了{Xn}为一独立随机变量序列,并且是一时间齐次Markov链。最后,利用该Markov链{Xn}的性质,证明了入圈问题经过有限次插点, Cm 的任意一边上都至少插入一个新点。
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