Base 86: Maximum Iteration Sequences: Cycle Start

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 Max Steps Max Step Example
Cycle Start
11 max steps10
22 max steps20 → 1Ψ → Φ3
344 max steps100 → 0ΩΩ → ΨΩ1 → ΧΩ2 → ΦΩ3 → ΥΩ4 → ΤΩ5 → ΣΩ6 → ΡΩ7 → ΠΩ8 → ΟΩ9 → ΞΩA → ΝΩB → ΜΩC → ΛΩD → ΚΩE → ΙΩF → ΘΩG → ΗΩH → ΖΩI → ΕΩJ → ΔΩK → ΓΩL → ΒΩM → ΑΩN → zΩO → yΩP → xΩQ → wΩR → vΩS → uΩT → tΩU → sΩV → rΩW → qΩX → pΩY → oΩZ → nΩa → mΩb → lΩc → kΩd → jΩe → iΩf → hΩg → gΩh
47 max stepsB00W → WAΝs → ΓLΒM → heih → 3ΩΩΦ → Φ2Φ4 → ΤΠ76 → ΝΘFC
535 max stepsg0000 → fΩΩΩi → ieΩig → j1ΩΧf → ΨfΩh2 → ΧgΩg3 → ΦeΩi4 → ΥfΩh5 → ΤdΩj6 → ΣeΩi7 → ΡcΩk8 → ΠdΩj9 → ΟbΩlA → ΞcΩkB → ΝaΩmC → ΜbΩlD → ΛZΩnE → ΚaΩmF → ΙYΩoG → ΘZΩnH → ΗXΩpI → ΖYΩoJ → ΕWΩqK → ΔXΩpL → ΓVΩrM → ΒWΩqN → ΑUΩsO → zVΩrP → yTΩtQ → xUΩsR → wSΩuS → vTΩtT → uRΩvU → wQΩwS → xTΩtR → wTΩtS
6254 max steps2000ΩΩ → ΩΩ1Χ01 → ΩΨΥ311 → ΨΧΠ722 → ΦΥΘF44 → ΡΠrV88 → ΙΘLΒGG → srfhWW → ML1ΧΓΓ → Φhfhg4 → Ρ20ΨΧ8 → ΨΥΘF42 → ΦΠrV84 → ΡΘLΒG8 → ΙrfhWG → sL1ΧΓW → ΦhLΒg4 → Ρg0Ψh8 → ΨΙ0ΨF2 → ΨΦsU32 → ΦΣNz64 → ΡΜblC8 → Ιz9ΞOG → ΕsamVK → kNBΜΑe → Αd5ΣkO → Νc6ΡlC → ΛΑ8ΟNE → ΗwckRI → oV7Πsa → ΙNDΚΑG → wsckVS → UN7ΠΑu → ΙdPxkG → sY6ΡpW → ΛMGΗΒE → wqeiXS → UJ3ΥΕu → ΡlPxc8 → ΙY8ΟpG → ΗsGΗVI → qoMΑZY → eIEΙΖk → un5ΣaU → ΝQCΛxC → ΑyWqPO → cZJΔom → kF9ΞΙe → Εt5ΣUK → ΝkOydC → Αa6ΡnO → ΛcCΛlE → yw8ΟRQ → ΗYUspI → oOGΗza → qbDΚmY → wIAΝΖS → ΓnTtaM → gQCΛxi → yX1ΧqQ → ΦYIΕp4 → ΡmGΗb8 → ΙqAΝXG → ΓsIΕVM → mgMΑhc → eA0ΨΞk → ΨΔ5ΣK2 → ΦΝieB4 → ΡΒ3ΥM8 → ΡΙeiF8 → Ιt3ΥUG → ΡsOyV8 → ΙaMΑnG → seCΛjW → yM4ΤΒQ → ΟfXpiA → ΕI2ΦΖK → Τnjda6 → ΝD5ΣΛC → ΝΑwQNC → ΑdVrkO → cM6ΡΒm → Λf9ΞiE → Εw2ΦRK → ΤkUsd6 → ΝO6ΡzC → ΛΑamNE → wdBΜkS → ΑU6ΡtO → ΛcOylE → wa8ΟnS → ΗUCΛtI → yoOyZQ → aYEΙpo → uHDΚΗU → wpPxYS → YUGΗtq → qPHΖyY → oZHΖoa → oFDΚΙa → wtDΚUS → wUOytS → aUOyto → aPDΚyo → wZDΚoS → wUEΙtS → uUOytU → aQOyxo → aXDΚqo → wJDΚΕS → wlTtcS → UQ8Οxu → ΗXPxqI → oYIΕpa → mHDΚΗc → wp9ΞYS → ΕUGΗtK → qkOydY → aI6ΡΖo → ΛnDΚaE → xvCΛSR → yWSurQ → YSKΓvq → iTHΖug → oR1Χwa → ΦVDΚs4 → ΡwMΑR8 → ΙeUsjG → sO4ΤzW → ΟbLΒmA → ΕgAΝhK → Γk0ΨdM → Ψg6Ρh2 → ΦΛ0ΨD4 → ΨΡwQ72 → ΦΚVrE4 → ΡvLΒS8 → ΙgSuhG → sS0ΨvW → ΨTLΒu2 → ΦgQwh4 → ΡW0Ψr8 → ΨΙKΓF2 → ΦthfU4 → ΡP1Χy8 → ΦΙYoF4 → ΡtFΘU8 → ΙsOyVG → saMΑnW → eMCΛΒk → yf5ΣiQ → ΝY2ΦpC → ΤΑGΗN6 → ΝqckXC → ΑJ7ΠΕO → ΙlblcG → sA8ΟΞW → ΗΔLΒKI → ojfhea → E51ΧΤΛ → ΦΞvRA4 → ΡΔTtK8 → ΙjPxeG → sY4ΤpW → ΟMGΗΒA → ΕqeiXK → kJ3ΥΕe → Ρl5Σc8 → ΝΙ8ΟFC → ΗΑsUNI → odNzka → cE6ΡΚm → Λv9ΞSE → ΕwSuRK → kVRvse → UN5ΣΑu → ΝdPxkC → ΑY6ΡpO → ΛcGΗlE → wq8ΟXS → ΗUIΕtI → omOyba → aEAΝΚo → ΓvDΚSM → wgSuhS → US0Ψvu → ΨTPxu2 → ΦYQwp4 → ΡWGΗr8 → ΙqKΓXG → siIΕfW → mM2ΦΒc → Τf9Ξi6 → ΝΕ2ΦJC → ΤΑkcN6 → Νd7ΠkC → ΙΑ6ΡNG → ΛsckVE → wN7ΠΑS → ΙdTtkG → sQ6ΡxW → ΛXLΒqE → wgIΕhS → mU0Ψtc → ΨP9Ξy2 → ΦΕYoJ4 → ΡlFΘc8 → Ιs8ΟVG → ΗsMΑVI → oeMΑja → eE4ΤΚk → Οv5ΣSA → ΝΕSuJC → ΑlRvcO → cU8Οtm → ΗP9ΞyI → ΕoYoZK → kGEΙΘe → ur5ΣWU → ΝQKΓxC → ΑiWqfO → cK2ΦΔm → Τj9Ξe6 → ΝΕ4ΤJC → ΟΑkcNA → Εd7ΠkK → Ιk6ΡdG → Λs6ΡVE → ΛwMΑRE → weUsjS → UO4Τzu → ΟbPxmA → ΕYAΝpK → ΓkGΗdM → qg6ΡhY → ΛI0ΨΖE → ΨwmaR2 → ΦVBΜs4 → ΡΑMΑN8 → ΙeckjG → s84ΤΠW → ΟΘLΒGA → ΕrfhWK → kL1ΧΓe → Φh5Σg4 → ΡΝ0ΨB8 → ΨΙΑMF2 → ΦtdjU4 → ΡP5Σy8 → ΝΙYoFC → ΑtFΘUO → scOylW → aM8ΟΒo → ΗfDΚiI → wo2ΦZS
738 max steps1000003 → 30ΩΩΩΨΧ → ΩΦ1ΩΧ31 → ΨΨΣΩ512 → ΨΦΡΩ632 → ΧΥΞΩ943 → ΦΣΚΩD64 → ΥΟΔΩJ95 → ΤΛuΩSD6 → ΣΖhΩfI7 → ΡzPΩxO8 → ΠsZΩnV9 → ΟkIΩΕdA → ΞwQΩwRB → ΝnUΩsaC → ΜiHΩΖfD → ΛuPΩxTE → ΚlTΩtcF → ΙgGΩΗhG → ΘsPΩxVH → ΗiRΩvfI → ΖfFΩΘiJ → ΙoPΩxZG → ΘjNΩzeH → ΗkKΩΓdI → ΖmOΩybJ → ΕhMΩΑgK → ΔiJΩΔfL → ΕiNΩzfK → ΔhJΩΔgL → ΕiMΩΑfK → ΔiKΩΓfL → ΔiMΩΑfL → ΓhKΩΓgM → ΔgLΩΒhL → ΓiKΩΓfM → ΔgMΩΑhL → ΓhJΩΔgM → ΕhLΩΒgK