| Radix Character Encoding | ||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | A | B | C |
| Color Key | ||
|---|---|---|
| Orange | Fixed Point | number that becomes itself after one iteration |
| Green | Final Numbers | all numbers eventually reached, from all cycles |
| Purple | Cycle Start | iterations include entry into cycle, assuming it repeats |
| Red | Full Cycle | iterations include entire cycle, proving it repeats |
| Blue | Start Numbers | subset (optimization) of all numbers; minimal for full coverage |
| Gray | No Results | any calculation that has no results |
| Digits | # Start Numbers | # Fixed Points (excluding zero) |
# Cycles (including fixed) (excluding zero) |
Full Cycle Max Length |
Avg Steps including Cycle Start |
Max Steps including Cycle Start |
Avg Steps including Full Cycle |
Max Steps including Full Cycle |
# Final Numbers (excluding zero) |
|---|---|---|---|---|---|---|---|---|---|
| 2 | 91 | 0 fixed pts | 1 cycle | 3 nodes | 1.99 avg steps | 3 max steps | 4.57 avg steps | 6 max steps | 3 final numbers |
| 4 | 1,820 | 0 fixed pts | 3 cycles | 6 nodes | 2.05 avg steps | 4 max steps | 7.46 avg steps | 10 max steps | 15 final numbers |
| 6 | 18,564 | 1 fixed pt | 1 cycle | 1 node | 11.84 avg steps | 20 max steps | 12.84 avg steps | 21 max steps | 1 final number |
| 8 | 125,970 | 1 fixed pt | 2 cycles | 4 nodes | 9.44 avg steps | 24 max steps | 10.96 avg steps | 25 max steps | 5 final numbers |
| 10 | 646,646 | 1 fixed pt | 4 cycles | 9 nodes | 9.81 avg steps | 27 max steps | 13.24 avg steps | 28 max steps | 19 final numbers |
| 12 | 2,704,156 | 1 fixed pt | 3 cycles | 10 nodes | 10.83 avg steps | 28 max steps | 19.43 avg steps | 38 max steps | 13 final numbers |
| 14 | 9,657,700 | 2 fixed pts | 3 cycles | 15 nodes | 9.21 avg steps | 31 max steps | 22.40 avg steps | 46 max steps | 17 final numbers |
| 16 | 30,421,755 | 1 fixed pt | 3 cycles | 11 nodes | 18.83 avg steps | 55 max steps | 28.62 avg steps | 66 max steps | 20 final numbers |
| 18 | 86,493,225 | 1 fixed pt | 2 cycles | 12 nodes | 15.06 avg steps | 39 max steps | 26.40 avg steps | 51 max steps | 13 final numbers |
| 20 | 225,792,840 | 2 fixed pts | 5 cycles | 12 nodes | 12.32 avg steps | 29 max steps | 21.34 avg steps | 41 max steps | 24 final numbers |
| 22 | 548,354,040 | 1 fixed pt | 4 cycles | 12 nodes | 14.83 avg steps | 42 max steps | 23.65 avg steps | 47 max steps | 22 final numbers |
| 24 | 1,251,677,700 | 1 fixed pt | 3 cycles | 12 nodes | 21.79 avg steps | 51 max steps | 33.25 avg steps | 63 max steps | 21 final numbers |
| 26 | 2,707,475,148 | 1 fixed pt | 3 cycles | 12 nodes | 18.71 avg steps | 53 max steps | 26.79 avg steps | 65 max steps | 15 final numbers |
| 28 | 5,586,853,480 | 2 fixed pts | 4 cycles | 12 nodes | 25.60 avg steps | 61 max steps | 37.27 avg steps | 73 max steps | 21 final numbers |