Spoiler:
Let and consider the sets and . It is clear that . Therefore .
So the only candidates are of the form for some . We know that and . So we compare
with
Therefore the complete solution set is .
This is a chalenge question. It has been approved by Mr.Fantastic
Let , where n is a natural number. Find the natural numbers a for which Q(a)>Q(a+1)
Moderator edit: Approved Challenge question.