| Radix Character Encoding | |||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | A | B | C | D | E | F |
| G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V |
| 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 | 30 | 0 fixed pts | 0 cycles | 0 nodes | 0.97 avg steps | 1 max steps | 1.97 avg steps | 2 max steps | 0 final numbers |
| 2 | 465 | 0 fixed pts | 3 cycles | 5 nodes | 1.43 avg steps | 2 max steps | 6.17 avg steps | 7 max steps | 15 final numbers |
| 3 | 4,960 | 1 fixed pt | 1 cycle | 1 node | 7.21 avg steps | 16 max steps | 8.21 avg steps | 17 max steps | 1 final number |
| 4 | 40,920 | 1 fixed pt | 7 cycles | 4 nodes | 3.27 avg steps | 7 max steps | 6.82 avg steps | 11 max steps | 21 final numbers |
| 5 | 278,256 | 1 fixed pt | 2 cycles | 2 nodes | 9.85 avg steps | 17 max steps | 10.86 avg steps | 18 max steps | 3 final numbers |
| 6 | 1,623,160 | 1 fixed pt | 8 cycles | 47 nodes | 18.76 avg steps | 58 max steps | 56.75 avg steps | 105 max steps | 90 final numbers |
| 7 | 8,347,680 | 0 fixed pts | 1 cycle | 4 nodes | 12.54 avg steps | 21 max steps | 16.54 avg steps | 25 max steps | 4 final numbers |
| 8 | 38,608,020 | 1 fixed pt | 4 cycles | 10 nodes | 46.37 avg steps | 133 max steps | 56.36 avg steps | 143 max steps | 24 final numbers |
| 9 | 163,011,640 | 2 fixed pts | 3 cycles | 6 nodes | 14.46 avg steps | 36 max steps | 16.08 avg steps | 37 max steps | 8 final numbers |
| 10 | 635,745,396 | 1 fixed pt | 5 cycles | 90 nodes | 32.85 avg steps | 107 max steps | 112.11 avg steps | 197 max steps | 118 final numbers |
| 11 | 2,311,801,440 | 2 fixed pts | 4 cycles | 25 nodes | 19.74 avg steps | 48 max steps | 44.29 avg steps | 73 max steps | 31 final numbers |
| 12 | 7,898,654,920 | 1 fixed pt | 6 cycles | 70 nodes | 43.73 avg steps | 126 max steps | 97.87 avg steps | 196 max steps | 142 final numbers |