| Radix Character Encoding | ||||||||||
|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | A |
| 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 | # Cycles (excluding fixed) (excluding zero) |
# Fixed Points (cycle length 1) (excluding zero) |
Fixed Points (excluding zero) (bold = exactly 1 fixed point [excluding zero], no other cycles) |
|---|---|---|---|
| 1 | 0 cycles | 0 fixed pts | - |
| 2 | 0 cycles | 1 fixed pt | 37 |
| 3 | 1 cycle | 0 fixed pts | - |
| 4 | 2 cycles | 0 fixed pts | - |
| 5 | 1 cycle | 0 fixed pts | - |
| 6 | 1 cycle | 0 fixed pts | - |
| 7 | 2 cycles | 0 fixed pts | - |
| 8 | 2 cycles | 1 fixed pt | 74318764 |
| 9 | 1 cycle | 1 fixed pt | 9751A8532 |
| 10 | 4 cycles | 0 fixed pts | - |
| 11 | 3 cycles | 0 fixed pts | - |
| 12 | 3 cycles | 1 fixed pt | 764321887644 |
| 13 | 2 cycles | 0 fixed pts | - |
| 14 | 4 cycles | 0 fixed pts | - |
| 15 | 1 cycle | 0 fixed pts | - |
| 16 | 4 cycles | 1 fixed pt | 7664322188876444 |
| 17 | 2 cycles | 1 fixed pt | A9875430A97653211 |
| 18 | 5 cycles | 1 fixed pt | 99775521AA88553312 |
| 19 | 2 cycles | 1 fixed pt | AA9875430A976532101 |
| 20 | 5 cycles | 1 fixed pt | 76664322218888764444 |
| 21 | 2 cycles | 2 fixed pts | A987654320A9876543211, AAA9875430A9765321001 |
| 22 | 7 cycles | 0 fixed pts | - |
| 23 | 4 cycles | 2 fixed pts | AA987654320A98765432101, AAAA9875430A97653210001 |
| 24 | 6 cycles | 1 fixed pt | 766664322221888887644444 |
| 25 | 6 cycles | 3 fixed pts | A98766543220A988765443211, AAA987654320A987654321001, AAAAA9875430A976532100001 |
| 26 | 9 cycles | 1 fixed pt | A99877554320AA987655332111 |
| 27 | 10 cycles | 4 fixed pts | AA98766543220A9887654432101, AAAA987654320A9876543210001, AAAAAA9875430A9765321000001, 999777555221AAA888555333112 |
| 28 | 8 cycles | 2 fixed pts | AA99877554320AA9876553321101, 7666664322222188888876444444 |
| 29 | 16 cycles | 4 fixed pts | A9876665432220A98887654443211, AAA98766543220A98876544321001, AAAAA987654320A98765432100001, AAAAAAA9875430A97653210000001 |
| 30 | 10 cycles | 1 fixed pt | AAA99877554320AA98765533211001 |
| 31 | 23 cycles | 4 fixed pts | AA9876665432220A988876544432101, AAAA98766543220A988765443210001, AAAAAA987654320A987654321000001, AAAAAAAA9875430A976532100000001 |
| 32 | 9 cycles | 3 fixed pts | A99887755443310AA997766553322111, AAAA99877554320AA987655332110001, 76666664322222218888888764444444 |
| 33 | 30 cycles | 5 fixed pts | A987666654322220A9888876544443211, AAA9876665432220A9888765444321001, AAAAA98766543220A9887654432100001, AAAAAAA987654320A9876543210000001, AAAAAAAAA9875430A9765321000000001 |
| 34 | 10 cycles | 2 fixed pts | AA99887755443310AA9977665533221101, AAAAA99877554320AA9876553321100001 |
| 35 | 40 cycles | 6 fixed pts | AA987666654322220A98888765444432101, AAAA9876665432220A98887654443210001, AAAAAA98766543220A98876544321000001, A999877755543220AAA9887655533321111, AAAAAAAA987654320A98765432100000001, AAAAAAAAAA9875430A97653210000000001 |
| 36 | 10 cycles | 5 fixed pts | A9988776554433210AA99877665543322111, AAA99887755443310AA99776655332211001, 766666664322222221888888887644444444, AAAAAA99877554320AA98765533211000001, 9999777755552221AAAA8888555533331112 |
| 37 | 53 cycles | 7 fixed pts | A98766666543222220A988888765444443211, AAA987666654322220A988887654444321001, AAAAA9876665432220A988876544432100001, AAAAAAA98766543220A988765443210000001, AAAAAAAAA987654320A987654321000000001, AA999877755543220AAA98876555333211101, AAAAAAAAAAA9875430A976532100000000001 |
| 38 | 15 cycles | 3 fixed pts | AA9988776554433210AA998776655433221101, AAAA99887755443310AA997766553322110001, AAAAAAA99877554320AA987655332110000001 |
| 39 | 67 cycles | 7 fixed pts | AA98766666543222220A9888887654444432101, AAAA987666654322220A9888876544443210001, AAAAAA9876665432220A9888765444321000001, AAAAAAAA98766543220A9887654432100000001, AAAAAAAAAA987654320A9876543210000000001, AAA999877755543220AAA988765553332111001, AAAAAAAAAAAA9875430A9765321000000000001 |