A020988 and A007583 interleaved.

Terms

a(0) =0a(1) =1a(2) =2a(3) =3a(4) =10a(5) =11a(6) =42a(7) =43a(8) =170a(9) =171a(10) =682a(11) =683a(12) =2730a(13) =2731a(14) =10922a(15) =10923a(16) =43690a(17) =43691a(18) =174762a(19) =174763a(20) =699050a(21) =699051a(22) =2796202a(23) =2796203a(24) =11184810a(25) =11184811a(26) =44739242a(27) =44739243a(28) =178956970a(29) =178956971