Trajectory of 3 under map n->41n+1 if n odd, n->n/2 if n even.

Terms

a(0) =3a(1) =124a(2) =62a(3) =31a(4) =1272a(5) =636a(6) =318a(7) =159a(8) =6520a(9) =3260a(10) =1630a(11) =815a(12) =33416a(13) =16708a(14) =8354a(15) =4177a(16) =171258a(17) =85629a(18) =3510790a(19) =1755395a(20) =71971196a(21) =35985598a(22) =17992799a(23) =737704760a(24) =368852380a(25) =184426190a(26) =92213095