Suppose I have an infinite integer series like $Q=4N-3$ where $N = 1,2,3\dots$ In this case the series values Q are $1,5,9,$ etc. Is there a way to determine if an integer $K$ is a member of this series without testing each $N$ until $Q > K$? In this example, all of the $Q$ are odd so even integers are obviously eliminated. However, try a large odd $K$ like $K=1,111,111.$ One possibility is to find an initial $N$ that puts $Q$ fairly close to $K$. Then adjust $N$ (up or down as needed) until either $Q=K$ or $Q$ jumps over $K$. However, is there a one-step (exact) solution that avoids the hunting? (I am using this series as an example but I would like a general solution for any integer series.)
Thanks, Don C.