| 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 | # Full Cycles (excluding zero) |
Max Cycle Length |
Longest Full Cycles (excluding zero) (bold = exactly one cycle [excluding zero]) |
|---|---|---|---|
| 1 | 0 cycles | - | - |
| 2 | 2 cycles | 4 nodes | ⮎ 2D → A5 → 4B → 69 ⮌ |
| 3 | 1 cycle | (fixed) 1 node | ⮎ 7F8 ⮌ |
| 4 | 4 cycles | 6 nodes | ⮎ 1FFE → E0E2 → EB32 → C774 → 7FF8 → 8688 ⮌ |
| 5 | 3 cycles | 4 nodes | ⮎ A4FA6 → B3FB5 → C5F94 → B6F85 ⮌ |
| 6 | 6 cycles | 5 nodes | ⮎ 840EB8 → E6FF82 → D95963 → A42CB6 → A73B86 ⮌ |
| 7 | 3 cycles | 11 nodes | ⮎ B71FD85 → E83FB72 → DB3FB43 → CA6F854 → B73FB85 → C63FB94 → C84FA74 → B82FC75 → D73FB83 → CA3FB54 → C85F974 ⮌ |
| 8 | 8 cycles | 8 nodes | ⮎ A832CC76 → A940EB66 → E742CB82 → CA70E854 → E850EA72 → EC50EA32 → EC94A632 → C962C964 ⮌ |
| 9 | 5 cycles | 8 nodes | ⮎ CA40FEB54 → FA85F9751 → EA51FDA52 → EC84FA732 → DB82FC743 → DA83FB753 → CA62FC954 → D873FB873 ⮌ |
| 10 | 20 cycles | 8 nodes | ⮎ A8732CC876 → A9410EEB66 → ED742CB822 → CBA70E8544 → E8750EA872 → EC510EEA32 → EDC94A6322 → CB962C9644 ⮌ |
| 11 | 4 cycles | 9 nodes | ⮎ C9530FECA64 → FB873FB8741 → EC740FEB832 → FCB83FB7431 → EC973FB8632 → DB951FDA643 → EA963FB9652 → DB642FCB943 → DA874FA8753 ⮌ |
| 12 | 39 cycles | 8 nodes | ⮎ A87732CC8876 → A94110EEEB66 → EDD742CB8222 → CBBA70E85444 → E87750EA8872 → EC5110EEEA32 → EDDC94A63222 → CBB962C96444 ⮌ |
| 13 | 4 cycles | 4 nodes | ⮎ DA9851FDA7653 → EA8541FDBA752 → EC9652FCA9632 → DC9742FCB8633 ⮌ |
| 14 | 73 cycles | 8 nodes | ⮎ A877732CC88876 → A941110EEEEB66 → EDDD742CB82222 → CBBBA70E854444 → E877750EA88872 → EC51110EEEEA32 → EDDDC94A632222 → CBBB962C964444 ⮌ |
| 15 | 6 cycles | 15 nodes | ⮎ DA97541FDBA8653 → EA96541FDBA9652 → EC96542FCBA9632 → DC98642FCB97633 → DA98531FDCA7653 → EAA7541FDBA8552 → EC96552FCAA9632 → DC97542FCBA8633 → DA98641FDB97653 → EA96431FDCB9652 → ECA8642FCB97532 → DC98641FDB97633 → EAA8531FDCA7552 → ECA7552FCAA8532 → DC97552FCAA8633 ⮌ |
| 16 | 129 cycles | 8 nodes | ⮎ A8777732CC888876 → A9411110EEEEEB66 → EDDDD742CB822222 → CBBBBA70E8544444 → E8777750EA888872 → EC511110EEEEEA32 → EDDDDC94A6322222 → CBBBB962C9644444 ⮌ |
| 17 | 6 cycles | 2 nodes | ⮎ DC755541FDBAAA833 → EAA86552FCAA97552 ⮌ |
| 18 | 232 cycles | 8 nodes | ⮎ A87777732CC8888876 → A94111110EEEEEEB66 → EDDDDD742CB8222222 → CBBBBBA70E85444444 → E87777750EA8888872 → EC5111110EEEEEEA32 → EDDDDDC94A63222222 → CBBBBB962C96444444 ⮌ |
| 19 | 10 cycles | 6 nodes | ⮎ ECA876420FEDB987532 → FCCA86420FEDB975331 → FECA98641FDB9765311 → EEDA86431FDCB975212 → EDCBA8641FDB9754322 → ECBA87641FDB9875432 ⮌ |
| 20 | 411 cycles | 8 nodes | ⮎ A877777732CC88888876 → A941111110EEEEEEEB66 → EDDDDDD742CB82222222 → CBBBBBBA70E854444444 → E877777750EA88888872 → EC51111110EEEEEEEA32 → EDDDDDDC94A632222222 → CBBBBBB962C964444444 ⮌ |
| 21 | 20 cycles | 6 nodes | ⮎ ECA8764320FEDCB987532 → FCCA986420FEDB9765331 → FECA986431FDCB9765311 → EEDA986431FDCB9765212 → EDCBA86431FDCB9754322 → ECBA987641FDB98765432 ⮌ |
| 22 | 729 cycles | 8 nodes | ⮎ A8777777732CC888888876 → A9411111110EEEEEEEEB66 → EDDDDDDD742CB822222222 → CBBBBBBBA70E8544444444 → E8777777750EA888888872 → EC511111110EEEEEEEEA32 → EDDDDDDDC94A6322222222 → CBBBBBBB962C9644444444 ⮌ |
| 23 | 27 cycles | 6 nodes | ⮎ ECA87655420FEDBAA987532 → FCCA8655420FEDBAA975331 → FECA9865541FDBAA9765311 → EEDA8655431FDCBAA975212 → EDCBA865541FDBAA9754322 → ECBA8765541FDBAA9875432 ⮌ |
| 24 | 1,265 cycles | 8 nodes | ⮎ A87777777732CC8888888876 → A94111111110EEEEEEEEEB66 → EDDDDDDDD742CB8222222222 → CBBBBBBBBA70E85444444444 → E87777777750EA8888888872 → EC5111111110EEEEEEEEEA32 → EDDDDDDDDC94A63222222222 → CBBBBBBBB962C96444444444 ⮌ |
| 25 | 41 cycles | 6 nodes | ⮎ ECA876555420FEDBAAA987532 → FCCA86555420FEDBAAA975331 → FECA98655541FDBAAA9765311 → EEDA86555431FDCBAAA975212 → EDCBA8655541FDBAAA9754322 → ECBA87655541FDBAAA9875432 ⮌ |
| 26 | 2,150 cycles | 8 nodes | ⮎ A877777777732CC88888888876 → A941111111110EEEEEEEEEEB66 → EDDDDDDDDD742CB82222222222 → CBBBBBBBBBA70E854444444444 → E877777777750EA88888888872 → EC51111111110EEEEEEEEEEA32 → EDDDDDDDDDC94A632222222222 → CBBBBBBBBB962C964444444444 ⮌ |
| 27 | 62 cycles | 6 nodes | ⮎ ECA9999876420FEDB9876666532 → FCCA864333320FEDCCCCB975331 → FECA999998641FDB97666665311 → EEDA864333331FDCCCCCB975212 → EDCBA99998641FDB97666654322 → ECBA876433331FDCCCCB9875432 ⮌ |