Earliest sequence where a(a(n))=2^n.

Terms

a(0) =3a(1) =8a(2) =2a(3) =256a(4) =6a(5) =32a(6) =9a(7) =4a(8) =128a(9) =11a(10) =1024a(11) =13a(12) =4096a(13) =15a(14) =16384