[math-fun] Iterate, stop, restart

Hello Math-Fun, Start with n, then let n=2n and iterate. When the string n reappears, stop the iterations and restart the procedure with the smallest integer not yet in S. S = 1,2,4,8,16,stop,3,6,12,24,48,96,192,384,stop,5,10,20,40,80,160,320,640,1280,2560,stop,7,14,28,56,112,224,448,896,1792,stop,9,18,36,72,144,288,576,1152,2304,4608,9216,stop,11,22,44,88,... Question: is there a new n that will restart S at some point and _not_ lead to a new stop? Best, É. à+ É. Catapulté de mon aPhone