| Radix Character Encoding | |||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | A | B |
| 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) |
|---|---|---|---|---|---|---|---|---|---|
| 1 | 12 | 0 fixed pts | 0 cycles | 0 nodes | 0.92 avg steps | 1 max steps | 1.92 avg steps | 2 max steps | 0 final numbers |
| 3 | 364 | 1 fixed pt | 1 cycle | 1 node | 3.69 avg steps | 7 max steps | 4.69 avg steps | 8 max steps | 1 final number |
| 5 | 4,368 | 1 fixed pt | 2 cycles | 2 nodes | 6.65 avg steps | 12 max steps | 7.68 avg steps | 13 max steps | 3 final numbers |
| 7 | 31,824 | 1 fixed pt | 2 cycles | 9 nodes | 10.89 avg steps | 24 max steps | 19.49 avg steps | 33 max steps | 10 final numbers |
| 9 | 167,960 | 1 fixed pt | 4 cycles | 13 nodes | 6.60 avg steps | 18 max steps | 18.37 avg steps | 31 max steps | 24 final numbers |
| 11 | 705,432 | 2 fixed pts | 4 cycles | 21 nodes | 8.66 avg steps | 25 max steps | 23.83 avg steps | 46 max steps | 29 final numbers |
| 13 | 2,496,144 | 1 fixed pt | 4 cycles | 32 nodes | 8.15 avg steps | 21 max steps | 21.23 avg steps | 46 max steps | 46 final numbers |
| 15 | 7,726,160 | 2 fixed pts | 4 cycles | 8 nodes | 12.15 avg steps | 32 max steps | 19.85 avg steps | 40 max steps | 13 final numbers |
| 17 | 21,474,180 | 2 fixed pts | 4 cycles | 8 nodes | 14.09 avg steps | 38 max steps | 22.06 avg steps | 46 max steps | 18 final numbers |
| 19 | 54,627,300 | 2 fixed pts | 4 cycles | 13 nodes | 14.16 avg steps | 40 max steps | 26.84 avg steps | 53 max steps | 18 final numbers |
| 21 | 129,024,480 | 6 fixed pts | 9 cycles | 18 nodes | 12.91 avg steps | 45 max steps | 29.70 avg steps | 63 max steps | 44 final numbers |
| 23 | 286,097,760 | 4 fixed pts | 6 cycles | 23 nodes | 13.76 avg steps | 50 max steps | 36.32 avg steps | 73 max steps | 50 final numbers |
| 25 | 600,805,296 | 5 fixed pts | 8 cycles | 33 nodes | 14.26 avg steps | 55 max steps | 41.44 avg steps | 83 max steps | 71 final numbers |
| 27 | 1,203,322,288 | 5 fixed pts | 11 cycles | 43 nodes | 14.82 avg steps | 60 max steps | 44.75 avg steps | 93 max steps | 101 final numbers |
| 29 | 2,311,801,440 | 6 fixed pts | 19 cycles | 53 nodes | 14.99 avg steps | 65 max steps | 46.33 avg steps | 107 max steps | 152 final numbers |
| 31 | 4,280,561,376 | 5 fixed pts | 33 cycles | 63 nodes | 14.50 avg steps | 70 max steps | 43.74 avg steps | 130 max steps | 238 final numbers |
| 33 | 7,669,339,132 | 8 fixed pts | 62 cycles | 73 nodes | 13.51 avg steps | 75 max steps | 39.99 avg steps | 147 max steps | 383 final numbers |