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ASU 297 All Soviet Union MO 1980 n_{k+1} = n_k + P(n_k), product of digits

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July 19, 2019
product of digitsnumber theorySequence

Problem Statement

Let us denote with P(n)P(n) the product of all the digits of nn. Consider the sequence nk+1=nk+P(nk)n_{k+1} = n_k + P(n_k) Can it be unbounded for some n1n_1?
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