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We define a function by dsf[n] = a+ a+ ... + a where {a, a, ..., a} is the list of the digits of an integer n. Suppose we start with any positive integer n, and repeatedly apply the function dsf. We can then generate a sequence of integers a . This sequence will eventually enter into one of 8 kinds of loops. We could prove this fact using Mathematica. Many of ideas in this paper are proposed by students, and this research shows what High School students can achieve.
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