Start at n and iterate the map in A006368; a(n) is the smallest number in the trajectory.

Terms

a(0) =0a(1) =1a(2) =2a(3) =2a(4) =4a(5) =4a(6) =4a(7) =4a(8) =8a(9) =4a(10) =8a(11) =8a(12) =12a(13) =8a(14) =14a(15) =8a(16) =16a(17) =8a(18) =18a(19) =14a(20) =20a(21) =16a(22) =14a(23) =8a(24) =24a(25) =14a(26) =14a(27) =20a(28) =14a(29) =14