All the twist knots have genus 1

Since the twist knots shown are all alternating projections, the Seifert surfaces they produce will have minimal genus, and therefore the genus of each knot will be the same as the genus of its corresponding surface. We therefore wish to determine the genus of the Seifert surfaces for these knots.

From the diagrams of the twist knots, we see that the Seifert circles for these knots will look like the following:

For a twist knot with n crossings, there are n - 1 Seifert circles. Therefore, using the formula g = (s - c - 1)/2, we get g = (n - (n - 1) - 1)/2, or g = 2/2 = 1.