| Radix Character Encoding | |||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | A | B | C | D | E | F |
| 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 | 136 | 0 fixed pts | 2 cycles | 4 nodes | 1.38 avg steps | 2 max steps | 5.02 avg steps | 6 max steps | 8 final numbers |
| 4 | 3,876 | 0 fixed pts | 4 cycles | 6 nodes | 3.26 avg steps | 6 max steps | 7.87 avg steps | 12 max steps | 15 final numbers |
| 6 | 54,264 | 1 fixed pt | 6 cycles | 5 nodes | 11.92 avg steps | 31 max steps | 16.83 avg steps | 36 max steps | 21 final numbers |
| 8 | 490,314 | 0 fixed pts | 8 cycles | 8 nodes | 11.81 avg steps | 35 max steps | 17.42 avg steps | 39 max steps | 34 final numbers |
| 10 | 3,268,760 | 1 fixed pt | 20 cycles | 8 nodes | 10.22 avg steps | 31 max steps | 16.29 avg steps | 37 max steps | 88 final numbers |
| 12 | 17,383,860 | 3 fixed pts | 39 cycles | 8 nodes | 9.53 avg steps | 27 max steps | 15.52 avg steps | 35 max steps | 167 final numbers |
| 14 | 77,558,760 | 6 fixed pts | 73 cycles | 8 nodes | 10.12 avg steps | 37 max steps | 15.92 avg steps | 45 max steps | 304 final numbers |
| 16 | 300,540,195 | 7 fixed pts | 129 cycles | 8 nodes | 10.84 avg steps | 35 max steps | 16.52 avg steps | 41 max steps | 531 final numbers |
| 18 | 1,037,158,320 | 12 fixed pts | 232 cycles | 8 nodes | 11.70 avg steps | 44 max steps | 17.20 avg steps | 52 max steps | 926 final numbers |
| 20 | 3,247,943,160 | 15 fixed pts | 411 cycles | 8 nodes | 12.61 avg steps | 43 max steps | 18.04 avg steps | 49 max steps | 1,615 final numbers |
| 22 | 9,364,199,760 | 21 fixed pts | 729 cycles | 8 nodes | 13.51 avg steps | 52 max steps | 18.87 avg steps | 60 max steps | 2,824 final numbers |
| 24 | 25,140,840,660 | 29 fixed pts | 1,265 cycles | 8 nodes | 14.20 avg steps | 51 max steps | 19.50 avg steps | 57 max steps | 4,865 final numbers |
| 26 | 63,432,274,896 | 37 fixed pts | 2,150 cycles | 8 nodes | 15.01 avg steps | 60 max steps | 20.24 avg steps | 68 max steps | 8,255 final numbers |