A081883 Numbers n such that the number of steps needed to reach an integer starting with n-1/4 or n+1/4 and iterating the map x-->x*ceiling(x) is the same.

5, 9, 21, 37, 46, 49, 53, 69, 85, 101, 113, 117, 121, 133, 137, 149, 165, 174, 177, 181, 197, 213, 217, 229, 241, 245, 261, 265, 277, 293, 302, 305, 309, 313, 325, 341, 357, 369, 373, 389, 393, 405, 421, 430, 433, 437, 441, 453, 469, 485, 497, 501, 517, 521