MathDB
2015-2016 Spring OMO #13

Source:

March 29, 2016
Online Math Open

Problem Statement

For a positive integer nn, let f(n)f(n) be the integer formed by reversing the digits of nn (and removing any leading zeroes). For example f(14172)=27141f(14172)=27141. Define a sequence of numbers {an}n≥0\{a_n\}_{n\ge 0} by a0=1a_0=1 and for all i≥0i\ge 0, ai+1=11aia_{i+1}=11a_i or ai+1=f(ai)a_{i+1}=f(a_i) . How many possible values are there for a8a_8?
Proposed by James Lin
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