| 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 | # 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 | 2 cycles | 0 fixed pts | - |
| 3 | 0 cycles | 1 fixed pt | 7F8 |
| 4 | 4 cycles | 0 fixed pts | - |
| 5 | 3 cycles | 0 fixed pts | - |
| 6 | 5 cycles | 1 fixed pt | 87FF78 |
| 7 | 2 cycles | 1 fixed pt | C83FB74 |
| 8 | 8 cycles | 0 fixed pts | - |
| 9 | 3 cycles | 2 fixed pts | DA72FC853, 887FFF778 |
| 10 | 19 cycles | 1 fixed pt | FDB70E8421 |
| 11 | 3 cycles | 1 fixed pt | DA752FCA853 |
| 12 | 36 cycles | 3 fixed pts | FDB750EA8421, FFDB70E84201, 8887FFFF7778 |
| 13 | 3 cycles | 1 fixed pt | DA7552FCAA853 |
| 14 | 67 cycles | 6 fixed pts | FDB9730EC86421, FDB7550EAA8421, CB8743FFBB8744, FFDB750EA84201, CC8843FFBB7734, FFFDB70E842001 |
| 15 | 3 cycles | 3 fixed pts | ECA8641FDB97532, DA75552FCAAA853, 88887FFFFF77778 |
| 16 | 122 cycles | 7 fixed pts | FDB97530ECA86421, FDB75550EAAA8421, DCA8742FFCB87533, FFDB9730EC864201, FFDB7550EAA84201, FFFDB750EA842001, FFFFDB70E8420001 |
| 17 | 4 cycles | 2 fixed pts | ECA86541FDBA97532, DA755552FCAAAA853 |
| 18 | 220 cycles | 12 fixed pts | FDB975530ECAA86421, FDB997330ECC866421, FFDB97530ECA864201, DDAA7732FFCC885523, FDDBB7710EE8844221, FDB755550EAAAA8421, FFFDB9730EC8642001, FFDB75550EAAA84201, FFFDB7550EAA842001, FFFFDB750EA8420001, FFFFFDB70E84200001, 888887FFFFFF777778 |
| 19 | 7 cycles | 3 fixed pts | ECA865541FDBAA97532, ECA986431FDCB976532, DA7555552FCAAAAA853 |
| 20 | 396 cycles | 15 fixed pts | FDB9975330ECCA866421, FDB9755530ECAAA86421, DDAA77532FFCCA885523, FDDBB77510EEA8844221, FFDB975530ECAA864201, FFDB997330ECC8664201, FFFDB97530ECA8642001, FFDDBB7710EE88442201, FDB7555550EAAAAA8421, FFDB755550EAAAA84201, FFFFDB9730EC86420001, FFFDB75550EAAA842001, FFFFDB7550EAA8420001, FFFFFDB750EA84200001, FFFFFFDB70E842000001 |
| 21 | 13 cycles | 7 fixed pts | ECA9865431FDCBA976532, ECA8655541FDBAAA97532, DA75555552FCAAAAAA853, CCB887443FFFBBB877434, CBB877443FFFBBB887444, CCC888443FFFBBB777334, 8888887FFFFFFF7777778 |
| 22 | 708 cycles | 21 fixed pts | FDB99755330ECCAA866421, FDDBB775510EEAA8844221, FDDBB977310EEC88644221, FDB97555530ECAAAA86421, FDB99973330ECCC8666421, FFDB9975330ECCA8664201, DDAA775532FFCCAA885523, FFDB9755530ECAAA864201, FFDDBB77510EEA88442201, FFFDB975530ECAA8642001, FFFDB997330ECC86642001, FFFFDB97530ECA86420001, FFFDDBB7710EE884422001, FDB75555550EAAAAAA8421, FFDB7555550EAAAAA84201, FFFDB755550EAAAA842001, FFFFFDB9730EC864200001, FFFFDB75550EAAA8420001, FFFFFDB7550EAA84200001, FFFFFFDB750EA842000001, FFFFFFFDB70E8420000001 |
| 23 | 22 cycles | 5 fixed pts | ECA98655431FDCBAA976532, ECA86555541FDBAAAA97532, ECA99864331FDCCB9766532, DCCA887442FFFCBB8775333, DA755555552FCAAAAAAA853 |
| 24 | 1,236 cycles | 29 fixed pts | EDCAA876431FFDCB98755322, FDB997555330ECCAAA866421, FDB999753330ECCCA8666421, FDDBB9775310EECA88644221, FDDBB7755510EEAAA8844221, FFDDBB775510EEAA88442201, FFDDBB977310EEC886442201, FDB975555530ECAAAAA86421, FFDB99755330ECCAA8664201, FFDB97555530ECAAAA864201, FFFDB9975330ECCA86642001, FFFDB9755530ECAAA8642001, FFDB99973330ECCC86664201, FFFDDBB77510EEA884422001, FFFFDB975530ECAA86420001, DDAA7755532FFCCAAA885523, FFFFDB997330ECC866420001, FFFFFDB97530ECA864200001, FFFFDDBB7710EE8844220001, FDB755555550EAAAAAAA8421, FFDB75555550EAAAAAA84201, FFFDB7555550EAAAAA842001, FFFFDB755550EAAAA8420001, FFFFFFDB9730EC8642000001, FFFFFDB75550EAAA84200001, FFFFFFDB7550EAA842000001, FFFFFFFDB750EA8420000001, FFFFFFFFDB70E84200000001, 88888887FFFFFFFF77777778 |
| 25 | 35 cycles | 6 fixed pts | ECA998654331FDCCBA9766532, ECA865555541FDBAAAAA97532, ECA986555431FDCBAAA976532, FEDCBA876420FEDB987543211, DDCAA877432FFFCCB88755323, DA7555555552FCAAAAAAAA853 |
| 26 | 2,113 cycles | 37 fixed pts | EDCAA8765431FFDCBA98755322, FDDBB97755310EECAA88644221, FDDBB99773310EECC886644221, FDB9997553330ECCCAA8666421, FDB9975555330ECCAAAA866421, FFDDBB9775310EECA886442201, FFFDDBB775510EEAA884422001, FFDB997555330ECCAAA8664201, FDDBB77555510EEAAAA8844221, FFFDDBB977310EEC8864422001, FDB9755555530ECAAAAAA86421, FFDB999753330ECCCA86664201, FFFDB99755330ECCAA86642001, FDB9999733330ECCCC86666421, FFDDBB7755510EEAAA88442201, FFDB975555530ECAAAAA864201, FFFDB97555530ECAAAA8642001, FFFFDB9975330ECCA866420001, FDDDBBB777110EEE8884442221, FFFFDB9755530ECAAA86420001, FFFDB99973330ECCC866642001, FFFFDDBB77510EEA8844220001, DDAA77555532FFCCAAAA885523, FFFFFDB975530ECAA864200001, FFFFFDB997330ECC8664200001, FFFFFFDB97530ECA8642000001, FDB7555555550EAAAAAAAA8421, FFFFFDDBB7710EE88442200001, FFDB755555550EAAAAAAA84201, FFFDB75555550EAAAAAA842001, FFFFDB7555550EAAAAA8420001, FFFFFDB755550EAAAA84200001, FFFFFFFDB9730EC86420000001, FFFFFFDB75550EAAA842000001, FFFFFFFDB7550EAA8420000001, FFFFFFFFDB750EA84200000001, FFFFFFFFFDB70E842000000001 |
| 27 | 53 cycles | 9 fixed pts | FEDCBA8765420FEDBA987543211, ECA8655555541FDBAAAAAA97532, ECA9865555431FDCBAAAA976532, ECA9986554331FDCCBAA9766532, FFEDCBA876420FEDB9875432101, ECA9998643331FDCCCB97666532, DDDAAA777332FFFCCC888555223, DA75555555552FCAAAAAAAAA853, 888888887FFFFFFFFF777777778 |