Inverse Permutation (conjectured) of Catapult Sequence (A167161).

Terms

a(0) =0a(1) =1a(2) =8a(3) =2a(4) =3a(5) =6a(6) =4a(7) =5a(8) =17a(9) =152a(10) =7a(11) =41a(12) =10a(13) =9a(14) =11a(15) =19a(16) =12a(17) =21a(18) =13a(19) =14a(20) =25a(21) =15a(22) =27a(23) =16a(24) =22a(25) =18a(26) =57a(27) =39a(28) =20a(29) =159537