  The first problem of the 2017 Putnam competition was to characterize a set of
natural numbers closed under both the square-root map $n^2 \mapsto n$ and the
"add 5 and square" map $ n \mapsto (n+5)^2$. We reframe this as a problem on an
infinite directed graph, using this framing both to generalize the problem and
its solution, as well as to determine the first appearance of each number in
this set under a row-wise algorithm that outputs all its elements.
