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2016 Latvia National Olympiad 3rd Round Grade9Problem5

Source:

July 22, 2016
recursionalgebra

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. What are the 4 numbers that immediately follow sk=2016s_k = 2016 in this sequence?
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