Problem

Source: 2024 Czech and Slovak Olympiad III A p5

Tags: Sequence, algebra, recurrence relation, floor function



Let $(a_k)^{\infty}_{k=0}$ be a sequence of real numbers such that if $k$ is a non-negative integer, then $$a_{k+1} = 3a_k - \lfloor 2a_k \rfloor - \lfloor a_k \rfloor.$$Definitely all positive integers $n$ such that if $a_0 = 1/n$, then this sequence is constant after a certain term.