| 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 | # 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 | 1 cycle | 0 fixed pts | - |
| 3 | 0 cycles | 1 fixed pt | 5B6 |
| 4 | 2 cycles | 0 fixed pts | - |
| 5 | 1 cycle | 1 fixed pt | 83B74 |
| 6 | 1 cycle | 1 fixed pt | 65BB56 |
| 7 | 1 cycle | 1 fixed pt | 962B853 |
| 8 | 1 cycle | 2 fixed pts | A850A632, 873BB744 |
| 9 | 3 cycles | 1 fixed pt | 665BBB556 |
| 10 | 3 cycles | 1 fixed pt | 8843BB7734 |
| 11 | 2 cycles | 2 fixed pts | A8641B97532, 8773BBB7444 |
| 12 | 5 cycles | 2 fixed pts | B97530A86421, 6665BBBB5556 |
| 13 | 3 cycles | 1 fixed pt | 88743BBB77434 |
| 14 | 8 cycles | 4 fixed pts | 986532BB886533, 996632BB885523, BB97530A864201, 87773BBBB74444 |
| 15 | 2 cycles | 2 fixed pts | 888443BBB777334, 66665BBBBB55556 |
| 16 | 18 cycles | 2 fixed pts | BBB97530A8642001, 887743BBBB774434 |
| 17 | 2 cycles | 2 fixed pts | BA986530BA8653211, 877773BBBBB744444 |
| 18 | 36 cycles | 5 fixed pts | A98755310AA8664322, A9866431BB98755322, BBBB97530A86420001, 8887443BBBB7774334, 666665BBBBBB555556 |
| 19 | 2 cycles | 2 fixed pts | BBA986530BA86532101, 8877743BBBBB7744434 |
| 20 | 67 cycles | 4 fixed pts | A98765421BB997654322, BBBBB97530A864200001, 8777773BBBBBB7444444, 88884443BBBB77773334 |
| 21 | 3 cycles | 6 fixed pts | BBBA986530BA865321001, 988655332BBB888665333, 998665332BBB888655323, 999666332BBB888555223, 88877443BBBBB77744334, 6666665BBBBBBB5555556 |
| 22 | 117 cycles | 4 fixed pts | AA88664421BB9977553312, B9977553310AA886644221, BBBBBB97530A8642000001, 88777743BBBBBB77444434 |
| 23 | 2 cycles | 4 fixed pts | BA987654320BA9876543211, BBBBA986530BA8653210001, 87777773BBBBBBB74444444, 888874443BBBBB777743334 |
| 24 | 191 cycles | 5 fixed pts | A9876644321BB99877554322, BB9977553310AA8866442201, BBBBBBB97530A86420000001, 888777443BBBBBB777444334, 66666665BBBBBBBB55555556 |
| 25 | 3 cycles | 5 fixed pts | A9986664331BBB98875553222, BBA987654320BA98765432101, BBBBBA986530BA86532100001, 887777743BBBBBBB774444434, 8888844443BBBBB7777733334 |
| 26 | 303 cycles | 4 fixed pts | BBB9977553310AA88664422001, BBBBBBBB97530A864200000001, 877777773BBBBBBBB744444444, 8888774443BBBBBB7777443334 |
| 27 | 6 cycles | 5 fixed pts | A99876654321BBB998765543222, BBBA987654320BA987654321001, BBBBBBA986530BA865321000001, 8887777443BBBBBBB7774444334, 666666665BBBBBBBBB555555556 |
| 28 | 459 cycles | 10 fixed pts | BAA9886654320BBA987655332111, A9987755533110AAA88666443222, BBBB9977553310AA886644220001, 998866553332BBBB888866553323, 988865553332BBBB888866653333, 999966663332BBBB888855552223, 999866653332BBBB888865553223, BBBBBBBBB97530A8642000000001, 8877777743BBBBBBBB7744444434, 88888744443BBBBBB77777433334 |
| 29 | 13 cycles | 6 fixed pts | AA98866644321BBB9987755533212, A998776554221BBB9997665443222, BBBBA987654320BA9876543210001, BBBBBBBA986530BA8653210000001, 8777777773BBBBBBBBB7444444444, 88887774443BBBBBBB77774443334 |
| 30 | 675 cycles | 6 fixed pts | BBAA9886654320BBA9876553321101, BBBBB9977553310AA8866442200001, BBBBBBBBBB97530A86420000000001, 888888444443BBBBBB777777333334, 88877777443BBBBBBBB77744444334, 6666666665BBBBBBBBBB5555555556 |
| 31 | 28 cycles | 5 fixed pts | AA988766544221BBB99977655433212, BBBBBA987654320BA98765432100001, BBBBBBBBA986530BA86532100000001, 88777777743BBBBBBBBB77444444434, 888887744443BBBBBBB777774433334 |
| 32 | 967 cycles | 8 fixed pts | B999777555333110AAA8886664442221, A9998666643331BBBB98887555532222, BAA998866553310BBAA8866553322111, BBBAA9886654320BBA98765533211001, BBBBBB9977553310AA88664422000001, BBBBBBBBBBB97530A864200000000001, 87777777773BBBBBBBBBB74444444444, 888877774443BBBBBBBB777744443334 |
| 33 | 54 cycles | 8 fixed pts | AAA888666444221BBB999777555333112, BA99877655433210BAA98876654432211, A99877665443221BBB999877655443222, BBBBBBA987654320BA987654321000001, BBBBBBBBBA986530BA865321000000001, 888777777443BBBBBBBBB777444444334, 8888887444443BBBBBBB7777774333334, 66666666665BBBBBBBBBBB55555555556 |