Base 20: Summary: All Digit Sets

Blog: The First Pixel: Kaprekar's Constant 6174

Radix Character Encoding
0123456789ABCDEF
GHIJKLMNOPQRSTUV

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)
1200 fixed pts0 cycles0 nodes0.95 avg steps1 max steps1.95 avg steps2 max steps0 final numbers
22101 fixed pt 3 cycles6 nodes1.40 avg steps2 max steps5.66 avg steps8 max steps10 final numbers
31,5401 fixed pt 1 cycle 1 node 5.29 avg steps11 max steps6.29 avg steps12 max steps1 final number 
48,8551 fixed pt 2 cycles6 nodes4.93 avg steps10 max steps7.11 avg steps11 max steps7 final numbers
542,5040 fixed pts2 cycles4 nodes6.11 avg steps13 max steps10.09 avg steps17 max steps6 final numbers
6177,1002 fixed pts6 cycles17 nodes7.61 avg steps18 max steps18.77 avg steps35 max steps33 final numbers
7657,8001 fixed pt 2 cycles13 nodes7.60 avg steps21 max steps17.52 avg steps34 max steps14 final numbers
82,220,0750 fixed pts2 cycles11 nodes34.49 avg steps79 max steps40.81 avg steps90 max steps13 final numbers
96,906,9002 fixed pts6 cycles10 nodes15.97 avg steps40 max steps24.86 avg steps50 max steps28 final numbers
1020,030,0100 fixed pts4 cycles23 nodes29.03 avg steps79 max steps46.42 avg steps95 max steps70 final numbers
1154,627,3000 fixed pts2 cycles5 nodes19.91 avg steps54 max steps23.98 avg steps58 max steps9 final numbers
12141,120,5251 fixed pt 3 cycles28 nodes74.66 avg steps156 max steps92.83 avg steps172 max steps45 final numbers
13347,373,6000 fixed pts1 cycle 52 nodes20.52 avg steps63 max steps72.52 avg steps115 max steps52 final numbers
14818,809,2003 fixed pts5 cycles40 nodes115.72 avg steps267 max steps152.39 avg steps307 max steps55 final numbers
151,855,967,5201 fixed pt 3 cycles30 nodes16.15 avg steps54 max steps44.46 avg steps81 max steps58 final numbers
164,059,928,9500 fixed pts5 cycles138 nodes58.06 avg steps172 max steps112.78 avg steps217 max steps168 final numbers
178,597,496,6000 fixed pts4 cycles31 nodes16.84 avg steps59 max steps44.19 avg steps90 max steps70 final numbers