Earliest sequence with a(a(a(n))) = 2n.

Terms

a(0) =0a(1) =3a(2) =6a(3) =5a(4) =12a(5) =2a(6) =10a(7) =9a(8) =24a(9) =11a(10) =4a(11) =14a(12) =20a(13) =15a(14) =18a(15) =17a(16) =48a(17) =26a(18) =22a(19) =21a(20) =8a(21) =23a(22) =28a(23) =38a(24) =40a(25) =27a(26) =30a(27) =29a(28) =36a(29) =50