Base 107: 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)
11070 fixed pts0 cycles0 nodes0.99 avg steps1 max steps1.99 avg steps2 max steps0 final numbers
25,7781 fixed pt 3 cycles9 nodes3.07 avg steps4 max steps9.79 avg steps13 max steps13 final numbers
3209,9340 fixed pts1 cycle 2 nodes21.22 avg steps54 max steps23.22 avg steps56 max steps2 final numbers
45,773,1850 fixed pts26 cycles53 nodes1.78 avg steps4 max steps54.78 avg steps57 max steps1,378 final numbers
5128,164,7070 fixed pts1 cycle 4 nodes20.84 avg steps41 max steps24.84 avg steps45 max steps4 final numbers
62,392,407,8641 fixed pt 6 cycles90 nodes60.16 avg steps209 max steps124.74 avg steps299 max steps201 final numbers