Base 90: 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--
25 cycles12 nodes8Υ → ΛH → sZ → IΚ → qb → EΞ → yT → Ux → Sz → Wv → OΔ → en
31 cycle (fixed) 1 node iδj
427 cycles12 nodesM1βΗ → αjh4 → Φ1β8 → αΜF4 → ΦvV8 → ΝPΒG → wbpW → QDΞΓ → ΑbpS → YDΞu → ΑLΖS → kXti
52 cycles2 nodesjhδjj → jδδδi
66 cycles247 nodesKIGΛΚΙ → urndaY → MH9ΣΛΗ → ΙtjhYK → oL1βΗe → αl9Σg4 → ΦΙ4ΨJ8 → ΤΝocFA → ΙxBΠUK → ΕoSydO → gWAΡvm → ΗP5ΧΓM → ΡkcohC → ΕC2αΠO → ΨΔflO6 → Ρf5ΧmC → ΡΕ6ΦNC → ΟΕgkNE → Αh3ΩkS → ΦY2αt8 → ΨΝKΗF6 → ΡxlfUC → ΕT5ΧyO → ΡgUwlC → ΕS4ΨzO → ΤgWulA → ΙO4ΨΔK → ΤoemdA → ΙB7ΥΡK → ΝΖndMG → wj9ΣiW → ΙQ0γΒK → γoaqd2 → αGAΡΜ4 → ΦΗuWL8 → ΝlNΔgG → wg4ΨlW → ΤQ4ΨΒA → ΤΙaqJA → ΙpFΜcK → woCΟdW → ΓQAΡΒQ → ΗcaqpM → kGCΟΜi → Γv1βWQ → αcOΓp4 → ΦeCΟn8 → ΝΓ8ΤPG → ΛwcoVI → sRBΠΑa → ΕZHΚsO → sgIΙla → qI4ΨΚc → ΤrDΞaA → ΙΑGΛRK → uoYsdY → MKAΡΘΗ → ΗnjheM → k91βΤi → αΚ1βI4 → αΦqa74 → ΦΞFΜE8 → ΝzvVSG → wXPΒuW → cQMΕΒq → ibDΞqk → ΑF1βΝS → αxXtU4 → ΦTLΖy8 → ΝkUwhG → wS2αzW → ΨXPΒu6 → ΡcMΕpC → ΕiCΟjO → Γg0γlQ → γc4Ψp2 → αΤCΟ94 → ΦΚΒPI8 → ΝrbpaG → wHDΞΛW → ΑtPΒYS → cYKΗtq → mLDΞΗg → Αl5ΧgS → ΡY4ΨtC → ΤΕKΗNA → ΙmgkfK → o73ΩΦe → ΦΞ9ΣE8 → ΝΙySJG → wpVvcW → RPCΟΓΒ → ΓdZroQ → cIAΡΚq → ΗrDΞaM → ΑkGΛhS → uY2αtY → ΨMKΗΖ6 → ΡmiifC → Ε6δδΦO → ΧΔFΜO7 → ΟwemVE → ΑR7ΥΑS → ΝZXtsG → wMIΙΖW → qjPΒic → cE0γΞq → γzDΞS2 → αΑWuR4 → ΦZNΔs8 → ΝgIΙlG → wq4ΨbW → ΤQEΝΒA → ΙyaqTK → oVFΜwe → wR9ΣΑW → ΙZPΒsK → ocIΙpe → qD9ΣΟc → ΙΒDΞQK → ΑoaqdS → YGAΡΜu → ΗvLΖWM → ljOΓih → e40γΩo → γΥ9Σ82 → αΜΘJG4 → ΦvndW8 → ΝP9ΣΓG → ΙwcoVK → oRBΠΑe → ΕZ9ΣsO → ΙgIΙlK → qo4Ψdc → ΤEAΡΞA → ΙΗySLK → olVvge → QA4ΨΣΓ → ΤΘbpKA → ΙnDΞeK → Αo8ΤdS → ΛYAΡtI → ΗsKΗZM → mkIΙhg → q62αΧc → ΨΠDΞC6 → ΡΔzROC → ΕfXtmO → gM6ΦΖm → Οj5ΧiE → ΡΑ0γRC → γΕYsN2 → αhJΘk4 → Φo2αd8 → ΨΝAΡF6 → ΡΗwULC → ΕlRzgO → gY4Ψtm → ΤL5ΧΗA → ΡΙkgJC → Εp3ΩcO → ΦgCΟl8 → ΝΓ4ΨPG → ΤwcoVA → ΙRBΠΑK → ΕoYsdO → gKAΡΘm → Ηn5ΧeM → Ρk8ΤhC → ΛΕ2αNI → ΨsgkZ6 → ΡJ3ΩΙC → ΦΕocN8 → ΝhBΠkG → Εw2αVO → ΨgQΑl6 → Ρa4ΨrC → ΤΕGΛNA → ΙugkXK → oN3ΩΕe → Φh9Σk8 → ΝΙ2αJG → ΨwocV6 → ΡRBΠΑC → ΖΔYsON → ifJΘmk → o71βΦe → αΞ9ΣE4 → ΦΙySJ8 → ΝpVvcG → wQCΟΒW → ΓbPΒqQ → dbEΝqp → yFBΠΝU → ΕxTxUO → gUSyxm → WT5Χyw → ΡVPΒwC → ΕcQΑpO → gaCΟrm → ΓH5ΧΛQ → ΡtbpYC → ΕLDΞΗO → ΑlflgS → Y64ΨΧu → ΤΠLΖCA → ΙΔjhOK → of1βme → αA6ΦΣ4 → ΦΟΗKD8 → ΝΒlfQG → wb5ΧqW → ΡQEΝΒC → ΕyaqTO → gVFΜwm → wR5ΧΑW → ΡZPΒsC → ΕcIΙpO → qgCΟlc → ΓE4ΨΞQ → ΤzbpSA → ΙXDΞuK → ΑoMΕdS → iYAΡtk → ΗL1βΗM → αljhg4 → Φ51βΨ8 → αΣΜFA4 → ΦΘvVK8 → ΝnPΒeG → wc8ΤpW → ΛQCΟΒI → ΓsaqZQ → cJFΜΙq → wpDΞcW → ΑQCΟΒS → ΓbXtqQ → cMEΝΖq → yjDΞiU → ΑU0γxS → γYSyt2 → αWKΗv4 → ΦmOΓf8 → Νe6ΦnG → Οw8ΤVE → ΛΑQΑRI → saYsra
71 cycle 4 nodesΖiKδΗjN → ΘjMδΕiL → ΗlLδΖgM → ΗkOδΓhM