Golomb sequence

Discrete Mathematics Level 4

Golomb's sequence is a non-decreasing integer sequence where \(a_n\) is the number of times that \(n\) occurs in the sequence, starting with \(a_1 = 1\), and with the property that for \(n > 1\) each \(a_n\) is the unique integer which makes it possible to satisfy the condition. The sequence starts off as

\[ 1,2,2,3,3,4,4,4,5,5,5, 6, 6, 6,6, \ldots \]

How many times does 50 appear in this sequence?

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