Question: Let a1, a2, a3, ... be the integer sequence defined recursively by 1) a1 = 0; and 2) For n > 1, an = 1

Let a1, a2, a3, ... be the integer sequence defined recursively by
1) a1 = 0; and
2) For n > 1, an = 1 + a(n/2).
Find an explicit formula for an and prove that your formula is correct.

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We claim that a n log 2 n for all n Z Proof When n 1 we have a 1 0 0 log 2 1 ... View full answer

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