Base 77: Summary: Even Digit Sets

Blog: The First Pixel: Kaprekar's Constant 6174

Radix Character Encoding
0123456789ABCDEF
GHIJKLMNOPQRSTUV
WXYZabcdefghijkl
mnopqrstuvwxyzΑΒ
ΓΔΕΖΗΘΙΚΛΜΝΞΟΠΡΣ

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 # Start Numbers # Fixed Points
(excluding zero)
# Cycles
(including fixed)
(excluding zero)
Full Cycle
Max Length
Avg Steps
including
Cycle Start
Max Steps
including
Cycle Start
Avg Steps
including
Full Cycle
Max Steps
including
Full Cycle
# Final Numbers
(excluding zero)
23,0031 fixed pt 3 cycles12 nodes2.20 avg steps3 max steps11.40 avg steps15 max steps19 final numbers
41,581,5800 fixed pts27 cycles30 nodes1.80 avg steps4 max steps30.67 avg steps34 max steps703 final numbers
6350,161,8120 fixed pts4 cycles172 nodes77.07 avg steps236 max steps167.62 avg steps304 max steps251 final numbers