@cosmo: I am having trouble verifying the machines at that link. It seems to me that the repeated states are not occurring at record values of the tape head, which means they can’t be Translated Cyclers. Have I misunderstood something? If only they provided proper Verification Data!
I’ll let @sligocki jump in as he found those machines but I believe that his output contains verification data:
1RB 0LD 1RC 1LD 1LD 0RC 0LA 1LB | Lin_Recur 7129704 512 <536870912
I believe that 7,129,704 is the length of the period and 512 536,870,912 when the machines enters the period?