Question 178
We define the sequence $\left(a_{n}\right)_{n \geq 0}$ of integers by $a_{n}:=2^{n}+2^{\lfloor n / 2\rfloor}$. Show that there are infinitely many terms of the sequence that can be expressed as the sum of at least two distinct terms of the sequence, and also that there are infinitely many terms of the sequence that cannot be written in this way.