Let S be a subset of the natural numbers such that 0 \in S, and for all n \in \mathbb{N}, if n is in S, then both 2 n+1 and 3 n+2 are in S. What is the smallest number of elements S can have in the range \{0,1, \ldots, 2019\}?
Let S be a subset of the natural numbers such that 0 \in S, and for all n \in \mathbb{N}, if n is in S, then both 2 n+1 and 3 n+2 are in S. What is the smallest number of elements S can have in the range \{0,1, \ldots, 2019\}?