Base 68: 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)
1680 fixed pts0 cycles0 nodes0.99 avg steps1 max steps1.99 avg steps2 max steps0 final numbers
22,3461 fixed pt 3 cycles22 nodes1.47 avg steps2 max steps18.81 avg steps24 max steps34 final numbers
354,7401 fixed pt 1 cycle 1 node 14.39 avg steps35 max steps15.39 avg steps36 max steps1 final number 
4971,6350 fixed pts8 cycles4 nodes4.38 avg steps10 max steps8.08 avg steps14 max steps28 final numbers
513,991,5440 fixed pts2 cycles4 nodes14.08 avg steps29 max steps18.08 avg steps33 max steps6 final numbers
6170,230,4521 fixed pt 3 cycles29 nodes176.68 avg steps311 max steps205.64 avg steps340 max steps41 final numbers
71,799,579,0641 fixed pt 2 cycles19 nodes13.04 avg steps27 max steps29.61 avg steps46 max steps20 final numbers
816,871,053,7250 fixed pts2 cycles104 nodes254.70 avg steps562 max steps351.64 avg steps666 max steps187 final numbers