Algorithms for complementary sequences

Finding the n-th positive square number is easy, as it is simply $n^2$. But how do we find the complementary sequence, i.e. the n-th positive nonsquare number? For this case there is an explicit formula. However, for general constraints on a number, this is harder to find. In this brief note, we study how to compute the n-th integer that does (or does not) satisfy a certain condition. In particular, we consider it as a fixed point problem, relate it to the iterative method of Lambek and Moser, study a bisection approach to this problem and provide a new formula for the n-th non-k-th power.