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Occurences of subsequences in sequence (Croatian MO 2004 1st Grade P4)

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April 8, 2021
algebraSequence

Problem Statement

The sequence 1,2,3,4,0,9,6,9,4,8,7,…1,2,3,4,0,9,6,9,4,8,7,\ldots is formed so that each term, starting from the fifth, is the units digit of the sum of the previous four. (a) Do the digits 2,0,0,42,0,0,4 occur in the sequence in this order? (b) Will the initial digits 1,2,3,41,2,3,4 ever occur again in this order?
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