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- Feb 14, 2012

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Consider the sequence of numbers 4, 7, 1, 8, 9, 7, 6, ... For $n>2$, the $n$th term of the sequence is the units digit of the sum of the two previous terms. Let $S_n$ denote the sum of the first $n$ terms of this sequence. What is the smallest value of $n$ for which $S_n>10000$?

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