Golomb sequence

Probability Level 4

Golomb's sequence is a non-decreasing integer sequence where ana_n is the number of times that nn occurs in the sequence, starting with a1=1a_1 = 1, and with the property that for n>1n > 1 each ana_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, 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?

Image credit: Wikipedia Vic201401


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