Base 92: Maximum Iteration Sequences: Full Cycle

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
Full Cycle
12 max steps100
212 max steps20 → 1ε → γ3Ψ7ΟFyVYvkjε1γ3
348 max steps100 → 0ζζ → εζ1 → δζ2 → γζ3 → βζ4 → αζ5 → Ωζ6 → Ψζ7 → Χζ8 → Φζ9 → ΥζA → ΤζB → ΣζC → ΡζD → ΠζE → ΟζF → ΞζG → ΝζH → ΜζI → ΛζJ → ΚζK → ΙζL → ΘζM → ΗζN → ΖζO → ΕζP → ΔζQ → ΓζR → ΒζS → ΑζT → zζU → yζV → xζW → wζX → vζY → uζZ → tζa → sζb → rζc → qζd → pζe → oζf → nζg → mζh → lζi → kζj → jζkjζk
421 max steps300K → K2γΛ → αpd6 → ΤBΣC → ΘΕON → kfnk → 7ζζΨ → Ψ6Ψ8 → ΡΞFE → ΓxVS → aRΒuaJΚuqJΚeqBΣeΗBΣOΗhlOi3βmΨ3β8ΨΞF8ΟxVGyRΒWaRΒu
541 max stepsj0000 → iζζζl → lhζlj → m1ζδi → εiζk2 → δjζj3 → γhζl4 → βiζk5 → αgζm6 → Ωhζl7 → Ψfζn8 → Χgζm9 → ΦeζoA → ΥfζnB → ΤdζpC → ΣeζoD → ΡcζqE → ΠdζpF → ΟbζrG → ΞcζqH → ΝaζsI → ΜbζrJ → ΛZζtK → ΚaζsL → ΙYζuM → ΘZζtN → ΗXζvO → ΖYζuP → ΕWζwQ → ΔXζvR → ΓVζxS → ΒWζwT → ΑUζyU → zVζxV → yTζzW → ΑSζΑU → ΒVζxT → ΑVζxUzUζyVzTζzVΑTζzUΑVζxU
6308 max steps3000XΖ → ΖX2γwP → αgOΕn6 → Τg6ΨnC → ΡΗ6ΨNE → ΡΓikRE → Γb1δsS → γaGΝt4 → ΨwIΛX8 → ΟsOΕbG → ygGΝnW → wS6ΨΒY → ΡZNΖuE → ΓiKΙlS → oa2γtg → αJ7ΧΛ6 → ΤΟqcFC → ΗzDΠUO → ΓiUylS → aU2γzu → αVJΚy6 → ΤqSΑdC → ΗYCΡvO → ΕiMΗlQ → ke2γpk → αAζζΤ6 → ΩΥ5ΩA7 → ΤΡΙKDC → ΗΔnfQO → id7Χqm → ΟD3βΡG → ΨΔxVQ8 → ΟdRΒqG → yaCΡtW → ΕSIΛΒQ → seYupc → MGAΤΞΙ → ΙxlhWM → mR3βΓi → Ψb3βs8 → ΨΟGΝF8 → ΟzvXUG → yVNΖyW → iTRΒΑm → aX3βwu → ΨPJΚΕ8 → ΟqeodG → yD9ΥΡW → ΛΔRΒQK → qdZtqe → KDBΣΡΛ → ΗΔpdQO → idBΣqm → ΗD3βΡO → ΨΔhlQ8 → Οd3βqG → ΨyCΡV8 → ΟΕSΑPG → yfXvoW → SO8ΦΖΓ → ΝhZtmI → uK4αΚa → ΦpJΚeA → ΛqAΤdK → ΙqCΡdM → ΕmCΡhQ → Εe4αpQ → ΦeAΤpA → ΛΙAΤLK → ΙqmgdM → mD5ΩΡi → ΤΔ3βQC → ΨΗcqN8 → ΟjDΠkG → Γy0εVS → εaSΑt2 → γYIΛv4 → ΨsMΗb8 → ΟkGΝjG → yw0εXW → εSOΕΒ2 → γgYun4 → ΨM6ΨΘ8 → ΡΟkiFE → Γz1δUS → γaUyt4 → ΨUIΛz8 → ΟsUybG → yUGΝzW → wVRΒyY → aTNΖΑu → iXJΚwm → qP3βΕe → ΨfBΣo8 → ΟΗ8ΦNG → ΝyikVI → uT1δΑa → γXJΚw4 → ΨqOΕd8 → ΟgCΡnG → Εy6ΨVQ → ΡeSΑpE → ΓYAΤvS → ΙaMΗtM → mkIΛji → s40εβc → εΧFΞ82 → γΞxVG4 → ΨxRΒW8 → ΟaQΓtG → ycIΛrW → sSEΟΒc → ΑZFΞuU → yWKΙxW → oSQΓΒg → cZ7Χus → ΟLFΞΙG → zxmgWV → UR5ΩΓΑ → ΤbVxsC → ΗSGΝΒO → wiYulY → OM2γΘΗ → αlhli6 → Τ42γβC → αΧΖN86 → ΤΞhlGC → Ηx3βWO → ΨiQΓl8 → Οc2γrG → αyEΟV6 → ΤΑSΑTC → ΗYWwvO → iQMΗΔm → kd3βqk → ΨCζζΡ8 → ΧΣ5ΩC9 → ΤΝΕOHC → ΗvfnYO → iN7ΧΗm → Οj3βkG → Ψy0εV8 → εΟSΑF2 → γzXvU4 → ΨVNΖy8 → ΟiSΑlG → yY2γvW → αSMΗΒ6 → ΤkYujC → ΗM0εΘO → εlhli2 → γ42γβ4 → αΨΦ876 → ΤΠΜHEC → ΗΒtZSO → iZJΚum → qL3βΙe → ΨnBΣg8 → ΟΗ6ΨNG → ΡyikVE → ΓT1δΑS → γaWwt4 → ΨQIΛΔ8 → ΟscqbG → yHDΠΝW → ΓvRΒYS → bZMΗut → kLHΜΙk → umζζga → tn7Χgb → ΟI6ΨΜG → ΡysaVE → ΓTHΜΑS → uaWwta → QKIΛΚΕ → spdpec → GCAΤΣΟ → ΙΖxVOM → mhRΒmi → a53βαu → ΨΥJΚA8 → ΟΚpdKG → ypBΣeW → ΗSAΤΒO → ΙiYulM → mM2γΘi → αl3βi6 → ΨΤ2γB8 → αΟΗMF6 → ΤzjjUC → ΗUζζyO → Ζz7ΧUP → ΟgUynG → yU6ΨzW → ΡVRΒyE → ΓaSΑtS → aYIΛvu → sNJΚΗc → qjFΞke → yC0εΣW → εΖRΒO2 → γhZtm4 → ΨK4αΚ8 → ΦΟoeFA → Λz9ΥUK → ΛqUydK → qUCΡze → ΕVBΣyQ → ΗeSΑpO → iYAΤvm → ΙN3βΗM → Ψmikh8 → Ο51δαG → γΥxVA4ΨΚRΒK8ΟpZteGyKAΤΚWΙpRΒeMmaAΤtiΙJ3βΛMΨrlhc8ΟF3βΟGΨzxVU8ΟVRΒyGyaSΑtWYSIΛΒwsZNΖuciLFΞΙmyn3βgWΨS6ΨΒ8ΡΟYuFEΓzLΘUSmaUytiUJ3βΛΑΨrVxc8ΟSEΟΒGΑyYuVUWTLΘΑymXRΒwiaP3βΕuΨfJΚo8Οq8ΦdGΝyCΡVIΕuSΑZQeYKΙvqoNBΣΗgΗj7ΧkOΟi0εlGεy2γV2γαSΑ54ΨΥXvA8ΟΚNΖKGyphleWSB3βΤΓΨΘZtM8ΟlJΚiGyq2γdWαSCΡΒ6ΤΕYuPCΗfLΘoOmi8ΦliΝ42γβIαΧtZ86ΤΞJΚGCΗxpdWOiRBΣΓmΗb3βsOΨiGΝl8Οw2γXGαyOΕV6ΤgSΑnCΗY6ΨvOΡiMΗlEΓk2γjSαa0εt6εΤIΛB2γΘrbM4ΨlFΞi8Οy2γVGαySΑV6ΤYSΑvCΗYMΗvOkiMΗlkk2ζζγkδjfnk3α80εΧ6εΤΝGB2γΘvXM4ΨlNΖi8Οi2γlGαy2γV6αΤSΑB6ΤΘXvMCΗlNΖiOjh2γmlα51δα6γΥΣBA4ΨΚΖNK8ΟphleGyB3βΤWΨΘRΒM8ΟlZtiGyK2γΚWαpRΒe6ΤaAΤtCΙΗIΛNMsmikhcG51δαΟγΥxVA4
751 max steps700000k → k6ζζζΨk → Ωjiζkk7 → Ψf0ζεo8 → ζΦgζm91 → εΦdζp92 → δΥgζmA3 → γΣcζqC4 → βΟeζoF5 → αΛZζtJ6 → ΩΖaζsO7 → ΨzUζyU8 → ΧsUζyb9 → ΦrMζΗcA → ΥyTζzVB → ΤqTζzdC → ΣpLζΘeD → ΡwSζΑXE → ΠoSζΑfF → ΟnKζΙgG → ΞuRζΒZH → ΝmRζΒhI → ΜlJζΚiJ → ΛsQζΓbK → ΚkQζΓjL → ΙjIζΛkM → ΜoOζΕfJ → ΛnOζΕgK → ΚmNζΖhL → ΙmNζΖhM → ΘlNζΖiN → ΗkMζΗjO → ΘiMζΗlNΘkNζΖjNΗkLζΘjOΙjMζΗkMΘmMζΗhNΘkOζΕjNΗjKζΙkOΚkMζΗjLΙnMζΗgMΘmPζΔhNΗiLζΘlOΙjNζΖkMΘlLζΘiNΙkOζΕjMΘkKζΙjNΚlNζΖiLΙmMζΗhMΘmOζΕhNΗjMζΗkOΘiMζΗlN