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

Terms

a(0) =1a(1) =38a(2) =19a(3) =704a(4) =352a(5) =176a(6) =88a(7) =44a(8) =22a(9) =11a(10) =408a(11) =204a(12) =102a(13) =51a(14) =1888a(15) =944a(16) =472a(17) =236a(18) =118a(19) =59a(20) =2184a(21) =1092a(22) =546a(23) =273a(24) =10102a(25) =5051a(26) =186888a(27) =93444a(28) =46722a(29) =23361