Base 105: 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)
11050 fixed pts0 cycles0 nodes0.99 avg steps1 max steps1.99 avg steps2 max steps0 final numbers
25,5650 fixed pts1 cycle 26 nodes2.22 avg steps3 max steps27.51 avg steps29 max steps26 final numbers
3198,4850 fixed pts1 cycle 2 nodes20.84 avg steps53 max steps22.84 avg steps55 max steps2 final numbers
45,359,0951 fixed pt 124 cycles12 nodes1.78 avg steps4 max steps13.26 avg steps16 max steps1,326 final numbers
5116,828,2711 fixed pt 1 cycle 1 node 22.86 avg steps43 max steps23.86 avg steps44 max steps1 final number 
62,141,851,6350 fixed pts4 cycles342 nodes57.50 avg steps180 max steps355.31 avg steps522 max steps428 final numbers