Base 92: Cycles Sequences: Maximum Length Cycle Count

Blog: The First Pixel: Kaprekar's Constant 6174

Radix Character Encoding
0123456789ABCDEF
GHIJKLMNOPQRSTUV
WXYZabcdefghijkl
mnopqrstuvwxyzΑΒ
ΓΔΕΖΗΘΙΚΛΜΝΞΟΠΡΣ
ΤΥΦΧΨΩαβγδεζηθικ

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 # Full Cycles
(excluding zero)
Max Cycle
Length
Longest Full Cycles
(excluding zero)
(bold = exactly one cycle [excluding zero])
10 cycles--
27 cycles10 nodes6Ω → ΡD → ΓR → at → IΜ → sb → GΞ → wX → OΖ → gn
31 cycle (fixed) 1 node jζk
45 cycles11 nodesC3βΤ → ΨΖN8 → ΟhlG → y3βW → ΨRΒ8 → ΟZtG → yJΚW → qRΒe → aBΣu → ΗJΚO → qhle
52 cycles4 nodeszTζzV → ΑTζzU → ΑVζxU → zUζyV
618 cycles95 nodesG51δαΟ → γΥxVA4 → ΨΚRΒK8 → ΟpZteG → yKAΤΚW → ΙpRΒeM → maAΤti → ΙJ3βΛM → Ψrlhc8 → ΟF3βΟG → ΨzxVU8 → ΟVRΒyG → yaSΑtW → YSIΛΒw → sZNΖuc → iLFΞΙm → yn3βgW → ΨS6ΨΒ8 → ΡΟYuFE → ΓzLΘUS → maUyti → UJ3βΛΑ → ΨrVxc8 → ΟSEΟΒG → ΑyYuVU → WTLΘΑy → mXRΒwi → aP3βΕu → ΨfJΚo8 → Οq8ΦdG → ΝyCΡVI → ΕuSΑZQ → eYKΙvq → oNBΣΗg → Ηj7ΧkO → Οi0εlG → εy2γV2 → γαSΑ54 → ΨΥXvA8 → ΟΚNΖKG → yphleW → SB3βΤΓ → ΨΘZtM8 → ΟlJΚiG → yq2γdW → αSCΡΒ6 → ΤΕYuPC → ΗfLΘoO → mi8Φli → Ν42γβI → αΧtZ86 → ΤΞJΚGC → ΗxpdWO → iRBΣΓm → Ηb3βsO → ΨiGΝl8 → Οw2γXG → αyOΕV6 → ΤgSΑnC → ΗY6ΨvO → ΡiMΗlE → Γk2γjS → αa0εt6 → εΤIΛB2 → γΘrbM4 → ΨlFΞi8 → Οy2γVG → αySΑV6 → ΤYSΑvC → ΗYMΗvO → kiMΗlk → k2ζζγk → δjfnk3 → α80εΧ6 → εΤΝGB2 → γΘvXM4 → ΨlNΖi8 → Οi2γlG → αy2γV6 → αΤSΑB6 → ΤΘXvMC → ΗlNΖiO → jh2γml → α51δα6 → γΥΣBA4 → ΨΚΖNK8 → ΟphleG → yB3βΤW → ΨΘRΒM8 → ΟlZtiG → yK2γΚW → αpRΒe6 → ΤaAΤtC → ΙΗIΛNM → smikhc
72 cycles19 nodesΗiLζΘlO → ΙjNζΖkM → ΘlLζΘiN → ΙkOζΕjM → ΘkKζΙjN → ΚlNζΖiL → ΙmMζΗhM → ΘmOζΕhN → ΗjMζΗkO → ΘiMζΗlN → ΘkNζΖjN → ΗkLζΘjO → ΙjMζΗkM → ΘmMζΗhN → ΘkOζΕjN → ΗjKζΙkO → ΚkMζΗjL → ΙnMζΗgM → ΘmPζΔhN