MathDB

N3

Part of 2018 IMO Shortlist

Problems(1)

Expressing a term of the sequence by the sum of previous terms

Source: ISL 2018 N3

7/17/2019
Define the sequence a_0,a_1,a_2,\hdots by an=2n+2⌊n/2⌋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.
IMO Shortlistnumber theory