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2016 Latvia National Olympiad 3rd Round Grade11Problem4

Source:

July 22, 2016
recursionnumber theory

Problem Statement

The integer sequence (si)(s_i) "having pattern 2016'" is defined as follows: ∘\circ The first member s1s_1 is 2. ∘\circ The second member s2s_2 is the least positive integer exceeding s1s_1 and having digit 0 in its decimal notation. ∘\circ The third member s3s_3 is the least positive integer exceeding s2s_2 and having digit 1 in its decimal notation. ∘\circ The third member s3s_3 is the least positive integer exceeding s2s_2 and having digit 6 in its decimal notation. The following members are defined in the same way. The required digits change periodically: 2→0→1→6→2→0→…2 \rightarrow 0 \rightarrow 1 \rightarrow 6 \rightarrow 2 \rightarrow 0 \rightarrow \ldots. The first members of this sequence are the following: 2;10;11;16;20;30;31;36;42;502; 10; 11; 16; 20; 30; 31; 36; 42; 50.\\ Does this sequence contain a) 2001, b) 2006?
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