IMO Shortlist 2018 problem N3


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3. listopada 2019.
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Define the sequence a_0,a_1,a_2,\hdots by a_n=2^n+2^{\lfloor n/2\rfloor}. Prove that there are infinitely many terms of the sequence which can be expressed as a sum of (two or more) distinct terms of the sequence, as well as infinitely many of those which cannot be expressed in such a way.

Izvor: https://www.imo-official.org/problems/IMO2018SL.pdf