Base 19: 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)
1190 fixed pts0 cycles0 nodes0.95 avg steps1 max steps1.95 avg steps2 max steps0 final numbers
21900 fixed pts1 cycle 2 nodes2.82 avg steps4 max steps4.57 avg steps6 max steps2 final numbers
31,3300 fixed pts1 cycle 2 nodes4.58 avg steps10 max steps6.56 avg steps12 max steps2 final numbers
47,3150 fixed pts4 cycles9 nodes1.97 avg steps4 max steps10.95 avg steps13 max steps36 final numbers
533,6490 fixed pts2 cycles4 nodes5.69 avg steps12 max steps9.00 avg steps15 max steps7 final numbers
6134,5960 fixed pts5 cycles6 nodes8.63 avg steps26 max steps12.60 avg steps28 max steps21 final numbers
7480,7000 fixed pts1 cycle 14 nodes8.43 avg steps19 max steps22.43 avg steps33 max steps14 final numbers
81,562,2750 fixed pts3 cycles5 nodes10.25 avg steps35 max steps15.21 avg steps40 max steps14 final numbers
94,686,8251 fixed pt 2 cycles2 nodes24.83 avg steps61 max steps26.82 avg steps63 max steps3 final numbers
1013,123,1101 fixed pt 5 cycles10 nodes10.43 avg steps32 max steps14.40 avg steps37 max steps25 final numbers
1134,597,2900 fixed pts2 cycles8 nodes27.31 avg steps62 max steps33.32 avg steps67 max steps13 final numbers
1286,493,2251 fixed pt 6 cycles9 nodes12.15 avg steps38 max steps14.79 avg steps41 max steps27 final numbers
13206,253,0750 fixed pts2 cycles21 nodes25.20 avg steps78 max steps46.16 avg steps99 max steps24 final numbers
14471,435,6002 fixed pts8 cycles5 nodes12.08 avg steps40 max steps14.64 avg steps43 max steps25 final numbers
151,037,158,3201 fixed pt 3 cycles63 nodes12.10 avg steps39 max steps66.62 avg steps102 max steps86 final numbers
162,203,961,4302 fixed pts11 cycles5 nodes11.49 avg steps34 max steps14.27 avg steps37 max steps34 final numbers
174,537,567,6500 fixed pts4 cycles31 nodes23.52 avg steps69 max steps50.88 avg steps100 max steps42 final numbers
189,075,135,3003 fixed pts17 cycles5 nodes11.60 avg steps38 max steps14.38 avg steps39 max steps50 final numbers