| Radix Character Encoding | |||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | A | B | C | D |
| 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 | 3 cycles | 4 nodes | ⮎ 0D → C1 → A3 → 67 ⮌ |
| 3 | 1 cycle | (fixed) 1 node | ⮎ 6D7 ⮌ |
| 4 | 1 cycle | 3 nodes | ⮎ 61B8 → A1B4 → A574 ⮌ |
| 5 | 2 cycles | 4 nodes | ⮎ 93D95 → A3D94 → A5D74 → 94D85 ⮌ |
| 6 | 4 cycles | 12 nodes | ⮎ 530CA9 → C73962 → A60C74 → C60C72 → CA0C32 → CA6632 → A6DD64 → 973965 → 640C98 → C51B82 → B92A43 → 974865 ⮌ |
| 7 | 1 cycle | 8 nodes | ⮎ A62DA74 → B63D973 → A82DA54 → B64D873 → A71DB64 → C73D962 → B92DA43 → B85D753 ⮌ |
| 8 | 4 cycles | 8 nodes | ⮎ 7550C887 → C32DDAA2 → BB8DD423 → BA72A633 → 9770C665 → C410CC92 → CBA48322 → A9739644 ⮌ |
| 9 | 3 cycles | 8 nodes | ⮎ A731DBA64 → C863D9752 → B941DB943 → C874D8652 → B831DBA53 → C884D8552 → B832DAA53 → B874D8653 ⮌ |
| 10 | 6 cycles | 6 nodes | ⮎ A8110CCC54 → CBB62A7222 → A9980C5444 → C6552A8872 → A8330CAA54 → C7762A7662 ⮌ |
| 11 | 3 cycles | 10 nodes | ⮎ A8730DCA654 → D9651DB8741 → CC741DB9612 → CBA72DA6322 → BA973D96433 → A8752DA8654 → B6531DBA873 → C8851DB8552 → CA632DAA732 → BA773D96633 ⮌ |
| 12 | 14 cycles | 12 nodes | ⮎ A74110CCC964 → CBB650C87222 → CA9930CA4432 → CA7754886632 → A74310CCA964 → CB7650C87622 → CA9310CCA432 → CBA774866322 → A97410CC9644 → CB6550C88722 → CA9330CAA432 → CA7774866632 ⮌ |
| 13 | 3 cycles | 17 nodes | ⮎ B96320DCBA743 → DA8862DA75531 → CB7531DBA8622 → CA9851DB85432 → CA8642DA97532 → BA7641DB97633 → C88630DCA7552 → DA9531DBA8431 → CC8763D976512 → CA9420DCB9432 → DAA864D875331 → CA7631DBA7632 → CA8740DC96532 → DA9641DB97431 → CC8652DA87512 → CAA531DBA8332 → CA8774D866532 ⮌ |
| 14 | 24 cycles | 12 nodes | ⮎ A743110CCCA964 → CBB7650C876222 → CA99310CCA4432 → CBA77548866322 → A974310CCA9644 → CB76550C887622 → CA93310CCAA432 → CBA77748666322 → A974110CCC9644 → CBB6550C887222 → CA99330CAA4432 → CA777548866632 ⮌ |
| 15 | 3 cycles | 13 nodes | ⮎ BA96310DCCA7433 → DB98762DA765421 → CB96420DCB97422 → DAA9752DA864331 → CB77641DB976622 → CA97310DCCA6432 → DBA9762DA764321 → CB97630DCA76422 → DAA8630DCA75331 → DC97751DB866411 → CCB7420DCB96212 → DBAA972DA643321 → CB97762DA766422 ⮌ |
| 16 | 42 cycles | 12 nodes | ⮎ A7411110CCCCC964 → CBBBB650C8722222 → CA999930CA444432 → CA77555488886632 → A7433310CCAAA964 → CB777650C8766622 → CA931110CCCCA432 → CBBBA77486632222 → A9997410CC964444 → CB655550C8888722 → CA933330CAAAA432 → CA77777486666632 ⮌ |
| 17 | 1 cycle | 32 nodes | ⮎ BA965310DCCA87433 → DB987641DB9765421 → CC975420DCB986412 → DBAA7541DB9863321 → CC987641DB9765412 → CBA75420DCB986322 → DAA98641DB9754331 → CC876541DB9876512 → CBA74320DCBA96322 → DAA98762DA7654331 → CB776420DCB976622 → DAA97310DCCA64331 → DCB97762DA7664211 → CCA96310DCCA74312 → DBBA9762DA7643221 → CB997630DCA764422 → DAA86530DCA875331 → DC977531DBA866411 → CCB86420DCB975212 → DBAA9741DB9643321 → CC987652DA8765412 → CAA64320DCBA97332 → DAA87762DA7665331 → CB775210DCCB86622 → DBAA9620DCB743321 → DCA98762DA7654311 → CCA76420DCB976312 → DBAA8630DCA753321 → DCA87751DB8665311 → CCB85320DCBA85212 → DBAA9852DA8543321 → CB977642DA9766422 ⮌ |
| 18 | 75 cycles | 12 nodes | ⮎ A74111110CCCCCC964 → CBBBBB650C87222222 → CA9999930CA4444432 → CA7755554888886632 → A74333310CCAAAA964 → CB7777650C87666622 → CA9311110CCCCCA432 → CBBBBA774866322222 → A99997410CC9644444 → CB6555550C88888722 → CA9333330CAAAAA432 → CA7777774866666632 ⮌ |
| 19 | 4 cycles | 25 nodes | ⮎ CAA643210DCCBA97332 → DBAA87762DA76653321 → CB9775210DCCB866422 → DBAA97420DCB9643321 → DCA987652DA87654311 → CCA764320DCBA976312 → DBAA87630DCA7653321 → DCA877520DCB8665311 → DCBA85320DCBA853211 → DCBA98752DA86543211 → CCA976431DBA9764312 → CBA876530DCA8765322 → DAA875320DCBA865331 → DCA877531DBA8665311 → CCB875320DCBA865212 → DBAA98531DBA8543321 → CC9877642DA97665412 → CAA654210DCCB987332 → DBAA87641DB97653321 → CC9876420DCB9765412 → DBAA75420DCB9863321 → DCA987641DB97654311 → CCB865420DCB9875212 → DBAA97431DBA9643321 → CC9877652DA87665412 ⮌ |
| 20 | 127 cycles | 12 nodes | ⮎ A741111110CCCCCCC964 → CBBBBBB650C872222222 → CA99999930CA44444432 → CA775555548888886632 → A743333310CCAAAAA964 → CB77777650C876666622 → CA93111110CCCCCCA432 → CBBBBBA7748663222222 → A999997410CC96444444 → CB65555550C888888722 → CA93333330CAAAAAA432 → CA777777748666666632 ⮌ |
| 21 | 3 cycles | 24 nodes | ⮎ CAA6432110DCCCBA97332 → DBBAA87762DA766533221 → CB99775210DCCB8664422 → DBAA975420DCB98643321 → DCA9876541DB987654311 → CCB8654320DCBA9875212 → DBAA986431DBA97543321 → CC98776541DB987665412 → CBA7543210DCCBA986322 → DBAA987641DB976543321 → CC98765420DCB98765412 → DBAA754320DCBA9863321 → DCA9877641DB976654311 → CCB8654210DCCB9875212 → DBBAA97431DBA96433221 → CC99877652DA876654412 → CAA6543210DCCBA987332 → DBAA877641DB976653321 → CC98764210DCCB9765412 → DBBAA75420DCB98633221 → DCA9987641DB976544311 → CCB8655420DCB98875212 → DBAA974331DBAA9643321 → CC98777652DA876665412 ⮌ |
| 22 | 211 cycles | 12 nodes | ⮎ A7411111110CCCCCCCC964 → CBBBBBBB650C8722222222 → CA999999930CA444444432 → CA77555555488888886632 → A7433333310CCAAAAAA964 → CB777777650C8766666622 → CA931111110CCCCCCCA432 → CBBBBBBA77486632222222 → A9999997410CC964444444 → CB655555550C8888888722 → CA933333330CAAAAAAA432 → CA77777777486666666632 ⮌ |
| 23 | 4 cycles | 14 nodes | ⮎ CBA97543210DCCBA9864322 → DBAA9876541DB9876543321 → CC987654320DCBA98765412 → DBAA8654320DCBA98753321 → DCA98776431DBA976654311 → CCB87654210DCCB98765212 → DBBAA974320DCBA96433221 → DCA99877652DA8766544311 → CCA76543210DCCBA9876312 → DBBAA876420DCB976533221 → DCA99876420DCB976544311 → DCBA8655420DCB988753211 → DCBA9864331DBAA97543211 → CCB98776541DB9876654212 ⮌ |
| 24 | 353 cycles | 12 nodes | ⮎ A74111111110CCCCCCCCC964 → CBBBBBBBB650C87222222222 → CA9999999930CA4444444432 → CA7755555554888888886632 → A74333333310CCAAAAAAA964 → CB7777777650C87666666622 → CA9311111110CCCCCCCCA432 → CBBBBBBBA774866322222222 → A99999997410CC9644444444 → CB6555555550C88888888722 → CA9333333330CAAAAAAAA432 → CA7777777774866666666632 ⮌ |
| 25 | 3 cycles | 11 nodes | ⮎ CBA755432110DCCCBA9886322 → DBBAA9876431DBA9765433221 → CC9987765420DCB9876654412 → DBAA75543210DCCBA98863321 → DCBA98776431DBA9766543211 → CCB987654210DCCB987654212 → DBBAA9754320DCBA986433221 → DCA998776541DB98766544311 → CCB865543210DCCBA98875212 → DBBAA9864331DBAA975433221 → CC9987776541DB98766654412 ⮌ |
| 26 | 557 cycles | 12 nodes | ⮎ A743333333110CCCAAAAAAA964 → CBB7777777650C876666666222 → CA99311111110CCCCCCCCA4432 → CBBBBBBBA77548866322222222 → A999999974310CCA9644444444 → CB76555555550C888888887622 → CA93333333310CCAAAAAAAA432 → CBA77777777748666666666322 → A974111111110CCCCCCCCC9644 → CBBBBBBBB6550C887222222222 → CA99999999330CAA4444444432 → CA777555555548888888866632 ⮌ |