Base 16: Final Numbers: Fixed Points

Blog: The First Pixel: Kaprekar's Constant 6174

Radix Character Encoding
0123456789ABCDEF

Color Key
OrangeFixed Pointnumber that becomes itself after one iteration
GreenFinal Numbersall numbers eventually reached, from all cycles
PurpleCycle Startiterations include entry into cycle, assuming it repeats
RedFull Cycleiterations include entire cycle, proving it repeats
BlueStart Numberssubset (optimization) of all numbers; minimal for full coverage
GrayNo Resultsany 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)
10 cycles0 fixed pts-
22 cycles0 fixed pts-
30 cycles1 fixed pt 7F8
44 cycles0 fixed pts-
53 cycles0 fixed pts-
65 cycles1 fixed pt 87FF78
72 cycles1 fixed pt C83FB74
88 cycles0 fixed pts-
93 cycles2 fixed ptsDA72FC853, 887FFF778
1019 cycles1 fixed pt FDB70E8421
113 cycles1 fixed pt DA752FCA853
1236 cycles3 fixed ptsFDB750EA8421, FFDB70E84201, 8887FFFF7778
133 cycles1 fixed pt DA7552FCAA853
1467 cycles6 fixed ptsFDB9730EC86421, FDB7550EAA8421, CB8743FFBB8744, FFDB750EA84201, CC8843FFBB7734, FFFDB70E842001
153 cycles3 fixed ptsECA8641FDB97532, DA75552FCAAA853, 88887FFFFF77778
16122 cycles7 fixed ptsFDB97530ECA86421, FDB75550EAAA8421, DCA8742FFCB87533, FFDB9730EC864201, FFDB7550EAA84201, FFFDB750EA842001, FFFFDB70E8420001
174 cycles2 fixed ptsECA86541FDBA97532, DA755552FCAAAA853
18220 cycles12 fixed ptsFDB975530ECAA86421, FDB997330ECC866421, FFDB97530ECA864201, DDAA7732FFCC885523, FDDBB7710EE8844221, FDB755550EAAAA8421, FFFDB9730EC8642001, FFDB75550EAAA84201, FFFDB7550EAA842001, FFFFDB750EA8420001, FFFFFDB70E84200001, 888887FFFFFF777778
197 cycles3 fixed ptsECA865541FDBAA97532, ECA986431FDCB976532, DA7555552FCAAAAA853
20396 cycles15 fixed ptsFDB9975330ECCA866421, FDB9755530ECAAA86421, DDAA77532FFCCA885523, FDDBB77510EEA8844221, FFDB975530ECAA864201, FFDB997330ECC8664201, FFFDB97530ECA8642001, FFDDBB7710EE88442201, FDB7555550EAAAAA8421, FFDB755550EAAAA84201, FFFFDB9730EC86420001, FFFDB75550EAAA842001, FFFFDB7550EAA8420001, FFFFFDB750EA84200001, FFFFFFDB70E842000001
2113 cycles7 fixed ptsECA9865431FDCBA976532, ECA8655541FDBAAA97532, DA75555552FCAAAAAA853, CCB887443FFFBBB877434, CBB877443FFFBBB887444, CCC888443FFFBBB777334, 8888887FFFFFFF7777778
22708 cycles21 fixed ptsFDB99755330ECCAA866421, FDDBB775510EEAA8844221, FDDBB977310EEC88644221, FDB97555530ECAAAA86421, FDB99973330ECCC8666421, FFDB9975330ECCA8664201, DDAA775532FFCCAA885523, FFDB9755530ECAAA864201, FFDDBB77510EEA88442201, FFFDB975530ECAA8642001, FFFDB997330ECC86642001, FFFFDB97530ECA86420001, FFFDDBB7710EE884422001, FDB75555550EAAAAAA8421, FFDB7555550EAAAAA84201, FFFDB755550EAAAA842001, FFFFFDB9730EC864200001, FFFFDB75550EAAA8420001, FFFFFDB7550EAA84200001, FFFFFFDB750EA842000001, FFFFFFFDB70E8420000001
2322 cycles5 fixed ptsECA98655431FDCBAA976532, ECA86555541FDBAAAA97532, ECA99864331FDCCB9766532, DCCA887442FFFCBB8775333, DA755555552FCAAAAAAA853
241,236 cycles29 fixed ptsEDCAA876431FFDCB98755322, 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
2535 cycles6 fixed ptsECA998654331FDCCBA9766532, ECA865555541FDBAAAAA97532, ECA986555431FDCBAAA976532, FEDCBA876420FEDB987543211, DDCAA877432FFFCCB88755323, DA7555555552FCAAAAAAAA853
262,113 cycles37 fixed ptsEDCAA8765431FFDCBA98755322, 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
2753 cycles9 fixed ptsFEDCBA8765420FEDBA987543211, ECA8655555541FDBAAAAAA97532, ECA9865555431FDCBAAAA976532, ECA9986554331FDCCBAA9766532, FFEDCBA876420FEDB9875432101, ECA9998643331FDCCCB97666532, DDDAAA777332FFFCCC888555223, DA75555555552FCAAAAAAAAA853, 888888887FFFFFFFFF777777778