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RU-ALLRUSSIAN 1980 Problem 14

    Define the sequence an\mathbf{a}_{\mathrm{n}} of positive integers as follows. a1=m\mathbf{a}_{1} = \mathbf{m} . an+1=an\mathbf{a}_{\mathrm{n} + 1} = \mathbf{a}_{\mathrm{n}} plus the product of the digits of an\mathbf{a}_{\mathrm{n}} . For example, if m=5\mathrm{m} = 5 , we have 5, 10, 10, ... . Is there an m for which the sequence is unbounded?

    Dataset text NuminaMath olympiads. Quoted with source.

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