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a_{n+1} = a_n+s(a_n), whereas s(a)=sum of digits of a

Source: JBMO 2008 Shortlist N3

October 14, 2017
sum of digitsJBMOnumber theory

Problem Statement

Let s(a)s(a) denote the sum of digits of a given positive integer a. The sequence a1,a2,...,an,...a_1, a_2,..., a_n, ... of positive integers is such that an+1=an+s(an)a_{n+1} = a_n+s(a_n) for each positive integer nn. Find the greatest possible n for which it is possible to have an=2008a_n = 2008.
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