Base 72: 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)
22,6280 fixed pts4 cycles9 nodes1.47 avg steps2 max steps10.25 avg steps11 max steps36 final numbers
41,215,4500 fixed pts2 cycles3 nodes6.62 avg steps17 max steps9.62 avg steps20 max steps6 final numbers
6237,093,7801 fixed pt 8 cycles47 nodes64.82 avg steps154 max steps84.07 avg steps170 max steps121 final numbers