A085817 Start at (2n+1)/4 and iterate the map x -> x*ceiling(x); sequence gives values of n for which the denominators in the orbit drop directly from 4 to 1, bypassing 2.

4, 6, 7, 9, 12, 13, 14, 15, 20, 21, 22, 23, 24, 30, 31, 36, 38, 39, 41, 44, 45, 46, 47, 52, 53, 54, 55, 56, 62, 63, 69, 70, 71, 73, 76, 77, 78, 79, 81, 86, 87, 88, 94, 95, 96, 97, 101, 102, 103, 105, 108, 109, 110, 111, 112, 118, 119, 120, 126, 127, 129, 132, 133, 134, 135, 137