A059994 Positions where number of periodic partitions increases.

2, 4, 5, 10, 16, 17, 31, 48, 79, 87, 111, 185, 187, 254, 259, 425, 432, 557, 627, 875, 922, 1173, 1232, 1262, 1776, 1927, 2446, 2592, 3485, 3881, 4655, 4775, 5122, 6657, 7399, 8843, 9068, 9794, 12546, 13738, 16439, 16876, 18398, 22522, 25136, 29546, 30842