Base 80: Summary: All 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)
1800 fixed pts0 cycles0 nodes0.99 avg steps1 max steps1.99 avg steps2 max steps0 final numbers
23,2401 fixed pt 4 cycles27 nodes1.48 avg steps2 max steps21.49 avg steps29 max steps40 final numbers
388,5601 fixed pt 1 cycle 1 node 16.65 avg steps41 max steps17.65 avg steps42 max steps1 final number 
41,837,6201 fixed pt 2 cycles5 nodes9.97 avg steps22 max steps11.30 avg steps23 max steps6 final numbers
530,872,0160 fixed pts2 cycles4 nodes16.14 avg steps33 max steps20.14 avg steps37 max steps6 final numbers
6437,353,5602 fixed pts7 cycles182 nodes44.61 avg steps121 max steps198.66 avg steps303 max steps251 final numbers
75,373,200,8801 fixed pt 2 cycles19 nodes14.77 avg steps31 max steps31.50 avg steps50 max steps20 final numbers