| Radix Character Encoding | |||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | A | B |
| 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 | 1 cycle | 6 nodes | ⮎ 0B → A1 → 83 → 47 → 29 → 65 ⮌ |
| 3 | 1 cycle | (fixed) 1 node | ⮎ 5B6 ⮌ |
| 4 | 2 cycles | 6 nodes | ⮎ 4198 → 8374 → 5287 → 6196 → 7BB4 → 7375 ⮌ |
| 5 | 2 cycles | 2 nodes | ⮎ 64B66 → 6BBB5 ⮌ |
| 6 | 2 cycles | 10 nodes | ⮎ 420A98 → A73742 → 842874 → 642876 → 62BB86 → 951963 → 860A54 → A40A72 → A82832 → 864654 ⮌ |
| 7 | 2 cycles | 9 nodes | ⮎ 841B974 → A53B762 → 971B943 → A64B652 → 960BA53 → B73B741 → A82B832 → 984B633 → 863B754 ⮌ |
| 8 | 3 cycles | 24 nodes | ⮎ 4210AA98 → A9737422 → 87428744 → 64328876 → 652BB866 → 961BB953 → A8428732 → 86528654 → 6410AA76 → A92BB822 → 9980A323 → A7646542 → 8320A984 → A7537642 → 8430A874 → A5428762 → 8630A854 → A540A762 → A830A832 → A8546632 → 8520A964 → A740A742 → A8328832 → 86546654 ⮌ |
| 9 | 4 cycles | 13 nodes | ⮎ 9630BA853 → B762B8541 → A941B9722 → A874B6432 → 9742B8743 → 9642B8753 → 9641B9753 → A651B9652 → A840BA732 → B873B7431 → A852B8632 → 9852B8633 → 9652B8653 ⮌ |
| 10 | 4 cycles | 5 nodes | ⮎ A8510AA632 → A9850A6322 → A8750A6432 → A8530A8632 → A8550A6632 ⮌ |
| 11 | 4 cycles | 21 nodes | ⮎ 97520BA9643 → B8651B96531 → AA630BA8512 → B9872B84321 → A9753B76422 → 98631B98533 → A6652B86552 → 98310BAA833 → B9764B65421 → A9530BA8622 → B8862B85331 → A9552B86622 → 98730BA8433 → B7653B76541 → A8320BA9832 → B8864B65331 → A8540BA7632 → B8741B97431 → AA642B87512 → A8841B97332 → A8653B76532 ⮌ |
| 12 | 7 cycles | 11 nodes | ⮎ 853320A98864 → A75540A76642 → A83310AA8832 → A98554666322 → 875210AA9644 → A97430A87422 → A87532886432 → 865530A86654 → A54110AAA762 → A99830A83222 → A87754664432 ⮌ |
| 13 | 4 cycles | 32 nodes | ⮎ 984210BAA9733 → B98663B755321 → A96520BA96522 → B88740BA74331 → BA7542B876411 → AA8431B987312 → A98653B765322 → 986520BA96533 → B86630BA85531 → BA7530BA86411 → BA9741B974211 → AA9752B864212 → A88741B974332 → A86542B876532 → 985420BA97633 → B86641B975531 → AA6420BA97512 → B98851B963321 → AA7652B865412 → A88420BA97332 → B88653B765331 → A85520BA96632 → B88630BA85331 → BA7552B866411 → AA8420BA97312 → B98863B753321 → A96551B966522 → A87410BAA7432 → B98742B874321 → A97542B876422 → 987431B987433 → A66542B876552 ⮌ |
| 14 | 12 cycles | 5 nodes | ⮎ A851110AAAA632 → A999850A632222 → A877750A644432 → A853330A888632 → A855550A666632 ⮌ |
| 15 | 4 cycles | 8 nodes | ⮎ A955420BA976622 → B887520BA964331 → BA86541B9765311 → AA96420BA975212 → B988751B9643321 → AA76541B9765412 → A985320BA986322 → B887652B8654331 ⮌ |
| 16 | 20 cycles | 5 nodes | ⮎ BB975310AA864201 → BB997530A8642201 → BB977530A8644201 → BB975330A8864201 → BB975530A8664201 ⮌ |
| 17 | 4 cycles | 8 nodes | ⮎ A8654320BA9876532 → B8865420BA9765331 → BA865420BA9765311 → BA986420BA9753211 → BA987641B97543211 → AA976431B98754212 → A9876431B98754322 → A8765431B98765432 ⮌ |
| 18 | 41 cycles | 5 nodes | ⮎ BBB975310AA8642001 → BBB997530A86422001 → BBB977530A86442001 → BBB975330A88642001 → BBB975530A86642001 ⮌ |
| 19 | 4 cycles | 13 nodes | ⮎ A98643320BA98875322 → B88765541B976654331 → AA6543210BAA9876512 → B99886420BA97533221 → BA8776541B976544311 → AA9643320BA98875212 → B98876541B976543321 → AA7654320BA98765412 → B98864320BA98753321 → BA8765541B976654311 → AA9643210BAA9875212 → B99887641B975433221 → AA7765431B987654412 ⮌ |
| 20 | 71 cycles | 5 nodes | ⮎ BBBB975310AA86420001 → BBBB997530A864220001 → BBBB977530A864420001 → BBBB975330A886420001 → BBBB975530A866420001 ⮌ |
| 21 | 9 cycles | 18 nodes | ⮎ A986433320BA988875322 → B887655541B9766654331 → AA65432110BAAA9876512 → B999886420BA975332221 → BA87776541B9765444311 → AA96433320BA988875212 → B988765541B9766543321 → AA76543210BAA98765412 → B998864320BA987533221 → BA87765541B9766544311 → AA96433210BAA98875212 → B998876541B9765433221 → AA77654320BA987654412 → B988643320BA988753321 → BA87655541B9766654311 → AA96432110BAAA9875212 → B999887641B9754332221 → AA77765431B9876544412 ⮌ |
| 22 | 121 cycles | 5 nodes | ⮎ BBBBB975310AA864200001 → BBBBB997530A8642200001 → BBBBB977530A8644200001 → BBBBB975330A8864200001 → BBBBB975530A8664200001 ⮌ |
| 23 | 6 cycles | 23 nodes | ⮎ AA965432110BAAA98765212 → B9998876420BA9754332221 → BA877765431B98765444311 → AA965433320BA9888765212 → B9887655420BA9766543321 → BA876543210BAA987654311 → BA998654320BA9876532211 → BA987765420BA9765443211 → BA987643320BA9887543211 → BA987655431B98766543211 → AA976543210BAA987654212 → B9988764320BA9875433221 → BA877655431B98766544311 → AA965433210BAA988765212 → B9988765420BA9765433221 → BA877654320BA9876544311 → BA986543320BA9887653211 → BA987655420BA9766543211 → BA987643210BAA987543211 → BA998765431B98765432211 → AA977654320BA9876544212 → B9887643320BA9887543321 → BA876555431B98766654311 ⮌ |
| 24 | 196 cycles | 5 nodes | ⮎ BBBBBB975310AA8642000001 → BBBBBB997530A86422000001 → BBBBBB977530A86442000001 → BBBBBB975330A88642000001 → BBBBBB975530A86642000001 ⮌ |
| 25 | 8 cycles | 33 nodes | ⮎ AA9654321110BAAAA98765212 → B99998876420BA97543322221 → BA8777765431B987654444311 → AA9654333320BA98888765212 → B98876555420BA97666543321 → BA8765432110BAAA987654311 → BA9998654320BA98765322211 → BA9877765420BA97654443211 → BA9876433320BA98887543211 → BA9876555431B987666543211 → AA9765432110BAAA987654212 → B99988764320BA98754332221 → BA8777655431B987665444311 → AA9654333210BAA9888765212 → B99887655420BA97665433221 → BA8776543210BAA9876544311 → BA9986543320BA98876532211 → BA9877655420BA97665443211 → BA9876433210BAA9887543211 → BA9987655431B987665432211 → AA9776543210BAA9876544212 → B99887643320BA98875433221 → BA8776555431B987666544311 → AA9654332110BAAA988765212 → B99988765420BA97654332221 → BA8777654320BA98765444311 → BA9865433320BA98887653211 → BA9876555420BA97666543211 → BA9876432110BAAA987543211 → BA9998765431B987654322211 → AA9777654320BA98765444212 → B98876433320BA98887543321 → BA8765555431B987666654311 ⮌ |
| 26 | 307 cycles | 5 nodes | ⮎ BBBBBBB975310AA86420000001 → BBBBBBB997530A864220000001 → BBBBBBB977530A864420000001 → BBBBBBB975330A886420000001 → BBBBBBB975530A866420000001 ⮌ |
| 27 | 11 cycles | 43 nodes | ⮎ AA96543211110BAAAAA98765212 → B999998876420BA975433222221 → BA87777765431B9876544444311 → AA96543333320BA988888765212 → B988765555420BA976666543321 → BA87654321110BAAAA987654311 → BA99998654320BA987653222211 → BA98777765420BA976544443211 → BA98764333320BA988887543211 → BA98765555431B9876666543211 → AA97654321110BAAAA987654212 → B999988764320BA987543322221 → BA87777655431B9876654444311 → AA96543333210BAA98888765212 → B998876555420BA976665433221 → BA87765432110BAAA9876544311 → BA99986543320BA988765322211 → BA98777655420BA976654443211 → BA98764333210BAA98887543211 → BA99876555431B9876665432211 → AA97765432110BAAA9876544212 → B999887643320BA988754332221 → BA87776555431B9876665444311 → AA96543332110BAAA9888765212 → B999887655420BA976654332221 → BA87776543210BAA98765444311 → BA99865433320BA988876532211 → BA98776555420BA976665443211 → BA98764332110BAAA9887543211 → BA99987655431B9876654322211 → AA97776543210BAA98765444212 → B998876433320BA988875433221 → BA87765555431B9876666544311 → AA96543321110BAAAA988765212 → B999988765420BA976543322221 → BA87777654320BA987654444311 → BA98654333320BA988887653211 → BA98765555420BA976666543211 → BA98764321110BAAAA987543211 → BA99998765431B9876543222211 → AA97777654320BA987654444212 → B988764333320BA988887543321 → BA87655555431B9876666654311 ⮌ |
| 28 | 469 cycles | 8 nodes | ⮎ AA88665443220BBA998776553312 → BA88866544220BBA997765533311 → BAA8866544220BBA997765533111 → BAA9886644220BBA997755332111 → BAA9887664421BB9977554332111 → AAA9876644321BB9987755432112 → AA98876644321BB9987755433212 → AA88766544321BB9987765543312 ⮌ |
| 29 | 19 cycles | 53 nodes | ⮎ AA965432111110BAAAAAA98765212 → B9999998876420BA9754332222221 → BA877777765431B98765444444311 → AA965433333320BA9888888765212 → B9887655555420BA9766666543321 → BA876543211110BAAAAA987654311 → BA999998654320BA9876532222211 → BA987777765420BA9765444443211 → BA987643333320BA9888887543211 → BA987655555431B98766666543211 → AA976543211110BAAAAA987654212 → B9999988764320BA9875433222221 → BA877777655431B98766544444311 → AA965433333210BAA988888765212 → B9988765555420BA9766665433221 → BA877654321110BAAAA9876544311 → BA999986543320BA9887653222211 → BA987777655420BA9766544443211 → BA987643333210BAA988887543211 → BA998765555431B98766665432211 → AA977654321110BAAAA9876544212 → B9999887643320BA9887543322221 → BA877776555431B98766654444311 → AA965433332110BAAA98888765212 → B9998876555420BA9766654332221 → BA877765432110BAAA98765444311 → BA999865433320BA9888765322211 → BA987776555420BA9766654443211 → BA987643332110BAAA98887543211 → BA999876555431B98766654322211 → AA977765432110BAAA98765444212 → B9998876433320BA9888754332221 → BA877765555431B98766665444311 → AA965433321110BAAAA9888765212 → B9999887655420BA9766543322221 → BA877776543210BAA987654444311 → BA998654333320BA9888876532211 → BA987765555420BA9766665443211 → BA987643321110BAAAA9887543211 → BA999987655431B98766543222211 → AA977776543210BAA987654444212 → B9988764333320BA9888875433221 → BA877655555431B98766666544311 → AA965433211110BAAAAA988765212 → B9999988765420BA9765433222221 → BA877777654320BA9876544444311 → BA986543333320BA9888887653211 → BA987655555420BA9766666543211 → BA987643211110BAAAAA987543211 → BA999998765431B98765432222211 → AA977777654320BA9876544444212 → B9887643333320BA9888887543321 → BA876555555431B98766666654311 ⮌ |
| 30 | 681 cycles | 13 nodes | ⮎ AA988664433220BBA9988775533212 → BA888766554421BB99776655433311 → AAA86654432210BBAA998776553112 → BA998886644220BBA9977553332211 → BAA88776654421BB99776554433111 → AAA98664433220BBA9988775532112 → BA988876654421BB99776554333211 → AAA87665443220BBA9987765543112 → BA988866443220BBA9987755333211 → BAA88766554421BB99776655433111 → AAA98664432210BBAA998775532112 → BA998887664421BB99775543332211 → AAA87766544321BB99877655443112 ⮌ |
| 31 | 33 cycles | 63 nodes | ⮎ AA9654321111110BAAAAAAA98765212 → B99999998876420BA97543322222221 → BA8777777765431B987654444444311 → AA9654333333320BA98888888765212 → B98876555555420BA97666666543321 → BA8765432111110BAAAAAA987654311 → BA9999998654320BA98765322222211 → BA9877777765420BA97654444443211 → BA9876433333320BA98888887543211 → BA9876555555431B987666666543211 → AA9765432111110BAAAAAA987654212 → B99999988764320BA98754332222221 → BA8777777655431B987665444444311 → AA9654333333210BAA9888888765212 → B99887655555420BA97666665433221 → BA8776543211110BAAAAA9876544311 → BA9999986543320BA98876532222211 → BA9877777655420BA97665444443211 → BA9876433333210BAA9888887543211 → BA9987655555431B987666665432211 → AA9776543211110BAAAAA9876544212 → B99999887643320BA98875433222221 → BA8777776555431B987666544444311 → AA9654333332110BAAA988888765212 → B99988765555420BA97666654332221 → BA8777654321110BAAAA98765444311 → BA9999865433320BA98887653222211 → BA9877776555420BA97666544443211 → BA9876433332110BAAA988887543211 → BA9998765555431B987666654322211 → AA9777654321110BAAAA98765444212 → B99998876433320BA98887543322221 → BA8777765555431B987666654444311 → AA9654333321110BAAAA98888765212 → B99998876555420BA97666543322221 → BA8777765432110BAAA987654444311 → BA9998654333320BA98888765322211 → BA9877765555420BA97666654443211 → BA9876433321110BAAAA98887543211 → BA9999876555431B987666543222211 → AA9777765432110BAAA987654444212 → B99988764333320BA98888754332221 → BA8777655555431B987666665444311 → AA9654333211110BAAAAA9888765212 → B99999887655420BA97665433222221 → BA8777776543210BAA9876544444311 → BA9986543333320BA98888876532211 → BA9877655555420BA97666665443211 → BA9876433211110BAAAAA9887543211 → BA9999987655431B987665432222211 → AA9777776543210BAA9876544444212 → B99887643333320BA98888875433221 → BA8776555555431B987666666544311 → AA9654332111110BAAAAAA988765212 → B99999988765420BA97654332222221 → BA8777777654320BA98765444444311 → BA9865433333320BA98888887653211 → BA9876555555420BA97666666543211 → BA9876432111110BAAAAAA987543211 → BA9999998765431B987654322222211 → AA9777777654320BA98765444444212 → B98876433333320BA98888887543321 → BA8765555555431B987666666654311 ⮌ |
| 32 | 975 cycles | 18 nodes | ⮎ AA9886644333220BBA99888775533212 → BA8887665554421BB997766655433311 → AAA866544322110BBAAA998776553112 → BA9998886644220BBA99775533322211 → BAA887776654421BB997765544433111 → AAA986644333220BBA99888775532112 → BA9888766554421BB997766554333211 → AAA876654432210BBAA9987765543112 → BA9988866443220BBA99877553332211 → BAA887766554421BB997766554433111 → AAA986644332210BBAA9988775532112 → BA9988876654421BB997765543332211 → AAA877665443220BBA99877655443112 → BA9888664433220BBA99887755333211 → BAA887665554421BB997766655433111 → AAA986644322110BBAAA998775532112 → BA9998887664421BB997755433322211 → AAA877766544321BB998776554443112 ⮌ |
| 33 | 62 cycles | 73 nodes | ⮎ AA96543211111110BAAAAAAAA98765212 → B999999998876420BA975433222222221 → BA87777777765431B9876544444444311 → AA96543333333320BA988888888765212 → B988765555555420BA976666666543321 → BA87654321111110BAAAAAAA987654311 → BA99999998654320BA987653222222211 → BA98777777765420BA976544444443211 → BA98764333333320BA988888887543211 → BA98765555555431B9876666666543211 → AA97654321111110BAAAAAAA987654212 → B999999988764320BA987543322222221 → BA87777777655431B9876654444444311 → AA96543333333210BAA98888888765212 → B998876555555420BA976666665433221 → BA87765432111110BAAAAAA9876544311 → BA99999986543320BA988765322222211 → BA98777777655420BA976654444443211 → BA98764333333210BAA98888887543211 → BA99876555555431B9876666665432211 → AA97765432111110BAAAAAA9876544212 → B999999887643320BA988754332222221 → BA87777776555431B9876665444444311 → AA96543333332110BAAA9888888765212 → B999887655555420BA976666654332221 → BA87776543211110BAAAAA98765444311 → BA99999865433320BA988876532222211 → BA98777776555420BA976665444443211 → BA98764333332110BAAA9888887543211 → BA99987655555431B9876666654322211 → AA97776543211110BAAAAA98765444212 → B999998876433320BA988875433222221 → BA87777765555431B9876666544444311 → AA96543333321110BAAAA988888765212 → B999988765555420BA976666543322221 → BA87777654321110BAAAA987654444311 → BA99998654333320BA988887653222211 → BA98777765555420BA976666544443211 → BA98764333321110BAAAA988887543211 → BA99998765555431B9876666543222211 → AA97777654321110BAAAA987654444212 → B999988764333320BA988887543322221 → BA87777655555431B9876666654444311 → AA96543333211110BAAAAA98888765212 → B999998876555420BA976665433222221 → BA87777765432110BAAA9876544444311 → BA99986543333320BA988888765322211 → BA98777655555420BA976666654443211 → BA98764333211110BAAAAA98887543211 → BA99999876555431B9876665432222211 → AA97777765432110BAAA9876544444212 → B999887643333320BA988888754332221 → BA87776555555431B9876666665444311 → AA96543332111110BAAAAAA9888765212 → B999999887655420BA976654332222221 → BA87777776543210BAA98765444444311 → BA99865433333320BA988888876532211 → BA98776555555420BA976666665443211 → BA98764332111110BAAAAAA9887543211 → BA99999987655431B9876654322222211 → AA97777776543210BAA98765444444212 → B998876433333320BA988888875433221 → BA87765555555431B9876666666544311 → AA96543321111110BAAAAAAA988765212 → B999999988765420BA976543322222221 → BA87777777654320BA987654444444311 → BA98654333333320BA988888887653211 → BA98765555555420BA976666666543211 → BA98764321111110BAAAAAAA987543211 → BA99999998765431B9876543222222211 → AA97777777654320BA987654444444212 → B988764333333320BA988888887543321 → BA87655555555431B9876666666654311 ⮌ |