Earliest sequence where a(a(n))=4^n.

Terms

a(0) =2a(1) =4a(2) =5a(3) =16a(4) =64a(5) =7a(6) =4096a(7) =9a(8) =65536a(9) =11a(10) =1048576a(11) =13a(12) =16777216a(13) =15a(14) =268435456a(15) =256a(16) =18a(17) =17179869184a(18) =20a(19) =274877906944a(20) =22a(22) =24a(24) =26a(26) =28a(28) =30a(30) =32