Base 108: Summary: All Digit Sets

Blog: The First Pixel: Kaprekar's Constant 6174

Radix Character Encoding
0123456789ABCDEF
GHIJKLMNOPQRSTUV
WXYZabcdefghijkl
mnopqrstuvwxyzΑΒ
ΓΔΕΖΗΘΙΚΛΜΝΞΟΠΡΣ
ΤΥΦΧΨΩαβγδεζηθικ
λμνξοπρςστυφχψωА

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)
11080 fixed pts0 cycles0 nodes0.99 avg steps1 max steps1.99 avg steps2 max steps0 final numbers
25,8860 fixed pts3 cycles18 nodes1.48 avg steps2 max steps19.17 avg steps20 max steps54 final numbers
3215,8201 fixed pt 1 cycle 1 node 21.91 avg steps55 max steps22.91 avg steps56 max steps1 final number 
45,989,0050 fixed pts10 cycles9 nodes4.10 avg steps10 max steps12.71 avg steps19 max steps78 final numbers
5134,153,7121 fixed pt 2 cycles2 nodes23.40 avg steps45 max steps24.40 avg steps46 max steps3 final numbers
62,526,561,5761 fixed pt 7 cycles176 nodes117.74 avg steps345 max steps233.26 avg steps521 max steps287 final numbers