A knot which is not alternating. Unlike alternating knots, flype moves are not sufficient to pass between all minimal diagrams of a given nonalternating knot (Hoste et al. 1998). In fact, Thistlethwaite used 13 different moves in generating a list of 16-crossing alternating knots (Hoste et al. 1998), and still had duplicates out of a list of knots (Hoste et al. 1998).
The numbers of nonalternating knots with , 2, ... crossings are 0, 0, 0, 0, 0, 0, 0, 3, 8, 42, 185, 888, ... (OEIS A051763), the first few of which are , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , and .