Lars Blomberg has discovered that if we start with any positive integer and repeatedly apply the map m -> A320486(m^2) then we will eventually either:
- reach 0,
- reach one of the four fixed points 1, 1465, 4376, 89476 (this sequence),
- reach the period-10 cycle shown in A321011, or
- reach the period-9 cycle shown in A321012.
From Lars Blomberg, Nov 17 2018: (Start)
Verified by testing all possible 8877690 start values that these are the only fixed points and cycles.
Detailed counts are:
- 561354 reach 0,
- 963738 reach one of the four fixed points 1, 1465, 4376, 89476 (counts 946109, 434, 17065, 130),
- 7271337 reach the period-10 cycle, and
- 81261 reach the period-9 cycle. (End)