| Radix Character Encoding | ||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | A | B | C | D | E |
| 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 | 15 | 0 fixed pts | 0 cycles | 0 nodes | 0.93 avg steps | 1 max steps | 1.93 avg steps | 2 max steps | 0 final numbers |
| 3 | 680 | 0 fixed pts | 1 cycle | 2 nodes | 3.79 avg steps | 8 max steps | 5.76 avg steps | 10 max steps | 2 final numbers |
| 5 | 11,628 | 1 fixed pt | 1 cycle | 1 node | 7.20 avg steps | 13 max steps | 8.20 avg steps | 14 max steps | 1 final number |
| 7 | 116,280 | 0 fixed pts | 2 cycles | 10 nodes | 6.11 avg steps | 13 max steps | 15.69 avg steps | 23 max steps | 18 final numbers |
| 9 | 817,190 | 1 fixed pt | 3 cycles | 8 nodes | 20.32 avg steps | 41 max steps | 27.93 avg steps | 49 max steps | 15 final numbers |
| 11 | 4,457,400 | 1 fixed pt | 4 cycles | 11 nodes | 12.89 avg steps | 37 max steps | 18.93 avg steps | 41 max steps | 25 final numbers |
| 13 | 20,058,300 | 1 fixed pt | 2 cycles | 4 nodes | 35.10 avg steps | 70 max steps | 39.10 avg steps | 74 max steps | 5 final numbers |
| 15 | 77,558,760 | 3 fixed pts | 7 cycles | 33 nodes | 12.99 avg steps | 34 max steps | 42.92 avg steps | 67 max steps | 48 final numbers |
| 17 | 265,182,525 | 1 fixed pt | 5 cycles | 11 nodes | 18.43 avg steps | 44 max steps | 24.52 avg steps | 49 max steps | 26 final numbers |
| 19 | 818,809,200 | 1 fixed pt | 4 cycles | 18 nodes | 12.49 avg steps | 30 max steps | 20.84 avg steps | 40 max steps | 32 final numbers |
| 21 | 2,319,959,400 | 1 fixed pt | 3 cycles | 11 nodes | 14.13 avg steps | 39 max steps | 22.33 avg steps | 47 max steps | 20 final numbers |
| 23 | 6,107,086,800 | 5 fixed pts | 7 cycles | 11 nodes | 12.36 avg steps | 36 max steps | 17.35 avg steps | 38 max steps | 18 final numbers |