Trajectory of 1 under map n->11n+1 if n odd, n->n/2 if n even.

Terms

a(0) =1a(1) =12a(2) =6a(3) =3a(4) =34a(5) =17a(6) =188a(7) =94a(8) =47a(9) =518a(10) =259a(11) =2850a(12) =1425a(13) =15676a(14) =7838a(15) =3919a(16) =43110a(17) =21555a(18) =237106a(19) =118553a(20) =1304084a(21) =652042a(22) =326021a(23) =3586232a(24) =1793116a(25) =896558a(26) =448279a(27) =4931070a(28) =2465535a(29) =27120886