Base 69: 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)
22,4150 fixed pts3 cycles12 nodes2.20 avg steps3 max steps11.08 avg steps15 max steps17 final numbers
41,028,7900 fixed pts29 cycles22 nodes1.80 avg steps4 max steps22.32 avg steps26 max steps561 final numbers
6185,250,7861 fixed pt 3 cycles39 nodes95.76 avg steps193 max steps134.70 avg steps232 max steps43 final numbers
818,855,883,5751 fixed pt 5 cycles7 nodes211.32 avg steps441 max steps218.29 avg steps448 max steps21 final numbers