| 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) |
|---|---|---|---|---|---|---|---|---|---|
| 1 | 16 | 0 fixed pts | 0 cycles | 0 nodes | 0.94 avg steps | 1 max steps | 1.94 avg steps | 2 max steps | 0 final numbers |
| 3 | 816 | 1 fixed pt | 1 cycle | 1 node | 4.50 avg steps | 9 max steps | 5.50 avg steps | 10 max steps | 1 final number |
| 5 | 15,504 | 0 fixed pts | 3 cycles | 4 nodes | 5.08 avg steps | 10 max steps | 8.37 avg steps | 13 max steps | 9 final numbers |
| 7 | 170,544 | 1 fixed pt | 3 cycles | 11 nodes | 4.86 avg steps | 11 max steps | 14.48 avg steps | 22 max steps | 21 final numbers |
| 9 | 1,307,504 | 2 fixed pts | 5 cycles | 8 nodes | 7.80 avg steps | 19 max steps | 14.94 avg steps | 26 max steps | 23 final numbers |
| 11 | 7,726,160 | 1 fixed pt | 4 cycles | 9 nodes | 10.53 avg steps | 24 max steps | 17.32 avg steps | 33 max steps | 21 final numbers |
| 13 | 37,442,160 | 1 fixed pt | 4 cycles | 4 nodes | 11.01 avg steps | 26 max steps | 14.37 avg steps | 30 max steps | 11 final numbers |
| 15 | 155,117,520 | 3 fixed pts | 6 cycles | 15 nodes | 14.72 avg steps | 40 max steps | 28.12 avg steps | 55 max steps | 22 final numbers |
| 17 | 565,722,720 | 2 fixed pts | 6 cycles | 2 nodes | 23.63 avg steps | 56 max steps | 24.73 avg steps | 57 max steps | 10 final numbers |
| 19 | 1,855,967,520 | 3 fixed pts | 10 cycles | 6 nodes | 24.13 avg steps | 56 max steps | 26.21 avg steps | 58 max steps | 21 final numbers |
| 21 | 5,567,902,560 | 7 fixed pts | 20 cycles | 6 nodes | 23.95 avg steps | 56 max steps | 26.43 avg steps | 58 max steps | 46 final numbers |
| 23 | 15,471,286,560 | 5 fixed pts | 27 cycles | 6 nodes | 25.93 avg steps | 66 max steps | 28.96 avg steps | 68 max steps | 83 final numbers |
| 25 | 40,225,345,056 | 6 fixed pts | 41 cycles | 6 nodes | 28.21 avg steps | 79 max steps | 31.56 avg steps | 81 max steps | 143 final numbers |
| 27 | 98,672,427,616 | 9 fixed pts | 62 cycles | 6 nodes | 30.34 avg steps | 82 max steps | 34.14 avg steps | 84 max steps | 229 final numbers |