Base 21: Final Numbers: Fixed Points

Blog: The First Pixel: Kaprekar's Constant 6174

Radix Character Encoding
0123456789ABCDEF
GHIJKLMNOPQRSTUV

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-
21 cycle 0 fixed pts-
31 cycle 0 fixed pts-
49 cycles0 fixed pts-
50 cycles1 fixed pt E6KD7
61 cycle 0 fixed pts-
73 cycles0 fixed pts-
83 cycles1 fixed pt ED6KKD77
93 cycles1 fixed pt HD93KGB74
101 cycle 1 fixed pt EE76KKDD67
113 cycles1 fixed pt EDD6KKKD777
122 cycles0 fixed pts-
133 cycles2 fixed ptsIFC962KHEB853, EED76KKKDD767
143 cycles2 fixed ptsGFB964KKFEB955, EDDD6KKKKD7777
151 cycle 1 fixed pt EEE776KKKDDD667
162 cycles1 fixed pt EEDD76KKKKDD7767