Trajectory of 3 under map n->37n+1 if n odd, n->n/2 if n even.

Terms

a(0) =3a(1) =112a(2) =56a(3) =28a(4) =14a(5) =7a(6) =260a(7) =130a(8) =65a(9) =2406a(10) =1203a(11) =44512a(12) =22256a(13) =11128a(14) =5564a(15) =2782a(16) =1391a(17) =51468a(18) =25734a(19) =12867a(20) =476080a(21) =238040a(22) =119020a(23) =59510a(24) =29755a(25) =1100936a(26) =550468a(27) =275234a(28) =137617a(29) =5091830