Base 76: 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)
1760 fixed pts0 cycles0 nodes0.99 avg steps1 max steps1.99 avg steps2 max steps0 final numbers
22,9260 fixed pts3 cycles30 nodes1.47 avg steps2 max steps25.44 avg steps32 max steps38 final numbers
376,0761 fixed pt 1 cycle 1 node 15.90 avg steps39 max steps16.90 avg steps40 max steps1 final number 
41,502,5010 fixed pts4 cycles9 nodes4.29 avg steps10 max steps13.29 avg steps19 max steps36 final numbers
524,040,0160 fixed pts3 cycles4 nodes15.88 avg steps31 max steps19.22 avg steps34 max steps9 final numbers
6324,540,2162 fixed pts5 cycles62 nodes146.64 avg steps284 max steps158.30 avg steps290 max steps76 final numbers
73,801,756,8161 fixed pt 2 cycles19 nodes14.20 avg steps30 max steps30.76 avg steps49 max steps20 final numbers