The [evenly spaced integer topology](https://en.wikipedia.org/wiki/Evenly_spaced_integer_topology) is countable, metrizable, and has no isolated points, and hence is homeomorphic to the rationals with the order topology. But what is an explicit construction for this homeomorphism?

This question was asked on MSE but got no answer: https://math.stackexchange.com/q/1849271/52694