Base 109: 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)
11090 fixed pts0 cycles0 nodes0.99 avg steps1 max steps1.99 avg steps2 max steps0 final numbers
25,9950 fixed pts3 cycles20 nodes2.22 avg steps3 max steps17.70 avg steps23 max steps27 final numbers
3221,8150 fixed pts1 cycle 2 nodes21.59 avg steps55 max steps23.59 avg steps57 max steps2 final numbers
46,210,8200 fixed pts81 cycles18 nodes1.78 avg steps4 max steps19.61 avg steps22 max steps1,431 final numbers
5140,364,5320 fixed pts2 cycles4 nodes22.03 avg steps42 max steps25.37 avg steps45 max steps7 final numbers
62,666,926,1080 fixed pts4 cycles176 nodes98.63 avg steps250 max steps232.65 avg steps419 max steps227 final numbers