this TM seems likely to eventually (after maybe on the order of 10^11 steps) enter a phase where its behavior can be described this way:```
A(16n+r) -> A(24n+s_r) for all large enough n
where s_r are constants for some 0<=r<16``` but not all r have corresponding s\_r. there are 4 values of r such that the TM does something different, which can in at least one case lead to completely breaking out of this cycle for an amount of time that might be exponential in n (or higher, potentially infinite or it might lead to halting). however, there might also be some sets of values of r that are inescapable, e.g. if for all odd r, s\_r was also odd, or if s\_0 and s\_8 are both 0 (mod 8). we don't know yet