| 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 | 27 | 0 fixed pts | 0 cycles | 0 nodes | 0.96 avg steps | 1 max steps | 1.96 avg steps | 2 max steps | 0 final numbers |
| 2 | 378 | 0 fixed pts | 1 cycle | 3 nodes | 2.90 avg steps | 4 max steps | 5.55 avg steps | 7 max steps | 3 final numbers |
| 3 | 3,654 | 0 fixed pts | 1 cycle | 2 nodes | 6.13 avg steps | 14 max steps | 8.12 avg steps | 16 max steps | 2 final numbers |
| 4 | 27,405 | 0 fixed pts | 10 cycles | 9 nodes | 1.90 avg steps | 4 max steps | 10.49 avg steps | 13 max steps | 78 final numbers |
| 5 | 169,911 | 1 fixed pt | 1 cycle | 1 node | 9.44 avg steps | 18 max steps | 10.44 avg steps | 19 max steps | 1 final number |
| 6 | 906,192 | 1 fixed pt | 4 cycles | 58 nodes | 8.61 avg steps | 33 max steps | 40.39 avg steps | 74 max steps | 73 final numbers |
| 7 | 4,272,048 | 0 fixed pts | 1 cycle | 8 nodes | 11.73 avg steps | 30 max steps | 19.73 avg steps | 38 max steps | 8 final numbers |
| 8 | 18,156,204 | 2 fixed pts | 7 cycles | 25 nodes | 13.82 avg steps | 42 max steps | 34.21 avg steps | 67 max steps | 64 final numbers |
| 9 | 70,607,460 | 1 fixed pt | 4 cycles | 8 nodes | 13.90 avg steps | 35 max steps | 19.48 avg steps | 43 max steps | 16 final numbers |
| 10 | 254,186,856 | 1 fixed pt | 2 cycles | 6 nodes | 38.78 avg steps | 83 max steps | 44.78 avg steps | 89 max steps | 7 final numbers |
| 11 | 854,992,152 | 1 fixed pt | 3 cycles | 15 nodes | 44.45 avg steps | 84 max steps | 59.20 avg steps | 99 max steps | 24 final numbers |
| 12 | 2,707,475,148 | 0 fixed pts | 6 cycles | 28 nodes | 21.61 avg steps | 74 max steps | 27.62 avg steps | 80 max steps | 52 final numbers |
| 13 | 8,122,425,444 | 1 fixed pt | 5 cycles | 41 nodes | 30.41 avg steps | 105 max steps | 68.28 avg steps | 146 max steps | 55 final numbers |