Dan, as a result of your message i am adding these two sequences to the OEIS. Comments or corrections welcomed! Neil %I A102421 %S A102421 1,7,1,1,5,25,7,17,19,43,1,13,7,61,1,35,37,79,5,11,23,97,25,53,55,115,7, %T A102421 31,1,133,17,71,73,151,19,5,41,169,43,89,91,187,1,49,25,205,13,107,109, %U A102421 223,7,29,59,241,61,125,127,259,1,67,17,277,35,143,145,295,37,19,77,313 %N A102421 Start with 2n+1, multiply by 3 and add 1 and divide out any power of 2; then mult\ iply by 3 and subtract 1 and divide out any power of 2. %C A102421 When a(x) is iterated, what are the limit cycles? Are there any besides (1) and (\ 17 -> 19 -> 43 -> 97 -> 109 -> 61)? %e A102421 n=1, 2n+1 = 3 -> 10 -> 5; 5 -> 14 ->7 = a(1). %O A102421 0,2 %K A102421 nonn %Y A102421 Cf. A102423. %p A102421 f:=proc(n) local j; j:=3*n+1; while j mod 2 = 0 do j:=j/2; od: j:=3*j-1; while j \ mod 2 = 0 do j:=j/2; od: j; end; %A A102421 njas, based on email from Dan Asimov (dasimov(AT)earthlink.net),Sep 15 2006 %I A102423 %S A102423 1,1,1,1,1,1,1,17,17,17,1 %N A102423 Start at 2n+1, iterate the map x -> A102421(x); sequence gives smallest number in\ resulting cycle, or -1 if the trajectory never cycles. %O A102423 0,8 %K A102423 nonn,more %A A102423 njas, based on email from Dan Asimov (dasimov(AT)earthlink.net), Sep 15 2006