Base 110: Maximum Iteration Sequences: Full Cycle

Blog: The First Pixel: Kaprekar's Constant 6174

Radix Character Encoding
0123456789ABCDEF
GHIJKLMNOPQRSTUV
WXYZabcdefghijkl
mnopqrstuvwxyzΑΒ
ΓΔΕΖΗΘΙΚΛΜΝΞΟΠΡΣ
ΤΥΦΧΨΩαβγδεζηθικ
λμνξοπρςστυφχψωА

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
238 max steps20 → 1χ → υ3ρ7ιFΡVΟXynγLΕhΓjΛbqvο9εJΙdmzΨPwpλDΦRstχ1υ3
357 max steps100 → 0ψψ → χψ1 → φψ2 → υψ3 → τψ4 → σψ5 → ςψ6 → ρψ7 → πψ8 → οψ9 → ξψA → νψB → μψC → λψD → κψE → ιψF → θψG → ηψH → ζψI → εψJ → δψK → γψL → βψM → αψN → ΩψO → ΨψP → ΧψQ → ΦψR → ΥψS → ΤψT → ΣψU → ΡψV → ΠψW → ΟψX → ΞψY → ΝψZ → Μψa → Λψb → Κψc → Ιψd → Θψe → Ηψf → Ζψg → Εψh → Δψi → Γψj → Βψk → Αψl → zψm → yψn → xψo → wψp → vψq → uψr → tψs → sψtsψt
427 max stepsE00f → fDκΘ → ΦRΥS → tqut → 3ψψυ → υ2υ4 → σπ76 → νθFCαΠVOΑjΒmIDκηΦΜZSsbΚuY1φΟυfΖ4ρPΧ8ιvpGΡ5ςWνjΒCαHζOΝzlacDκΛΦXΞSsfΖuQ1φΨυvp4ρ5ς8νθFC
547 max stepss0000 → rψψψu → uqψus → v1ψφr → χrψt2 → φsψs3 → υqψu4 → τrψt5 → σpψv6 → ςqψu7 → ρoψw8 → πpψv9 → οnψxA → ξoψwB → νmψyC → μnψxD → λlψzE → κmψyF → ιkψΑG → θlψzH → ηjψΒI → ζkψΑJ → εiψΓK → δjψΒL → γhψΔM → βiψΓN → αgψΕO → ΩhψΔP → ΨfψΖQ → ΧgψΕR → ΦeψΗS → ΥfψΖT → ΤdψΘU → ΣeψΗV → ΡcψΙW → ΠdψΘX → ΟbψΚY → ΞcψΙZ → ΝaψΛa → ΜbψΚb → ΛZψΜc → ΝYψΝa → ΞbψΚZ → ΝbψΚaΜaψΛbΜZψΜbΝZψΜaΝbψΚa
6464 max steps7000kΠ → Πk6ρΒX → λiGηΔE → ΦΟKγXS → ΗsgΕtg → QO0χΩΨ → χzvpm2 → υD5ςλ4 → ρνΦQB8 → ιβtrMG → ΡΔ1φiW → υkKγΒ4 → ρΗGηf8 → ιΟQΦXG → ΡugΕrW → kO2υΩΓ → σzHζm6 → νΝCλZC → αΨcΙPO → ΑxVΠom → kE8οκΓ → ηΥHζSI → ΞΜquaZ → eb3τΛΙ → ρZTΣΝ8 → ιocΙxG → ΡW8οΠW → ηkiΓΒI → ΝKGηδa → ΟΘbΚeY → gYSΤΞΗ → qfPΧΗw → wR5ςΦq → νt5ςsC → να0χNC → χαΑkN2 → υΒFθk4 → ρΡGηV8 → ιΟkΑXG → ΡhFθΕW → ΡkMαΒW → ΓkGηΒk → ΟIGηζY → ΟΜfΖaY → gbPΧΛΗ → wZPΧΝq → wd5ςΙq → νV5ςΡC → ναkΑNC → αΒFθkO → ΡΑGηlW → ΟkEιΒY → ΤgGηΖU → ΟoOΨxY → yg8οΖo → ηP9ξΨI → εΝwoZK → Ιd7πΙe → ιVTΣΡG → ΡokΑxW → kG8οθΓ → ηΠHζWI → ΞΜiΓaZ → ebJδΛΙ → ΙZTΣΝe → odTΣΙy → oV9ξΡy → εl9ξΑK → εΙEιdK → ΤΙUΡdU → omUΡzy → mD9ξλΑ → εΧDκQK → ΦΙuqdS → sV3τΡu → ρl1φΑ8 → υιEιF4 → ρΤΡUT8 → ιplzwG → ΡE6ρκW → λΥjΒSE → ΦrHζuS → Νs2υta → σc0χΚ6 → χνWΟB2 → υβhΔM4 → ρΔLβi8 → ιΕKγhG → ΡΗMαfW → ΓkQΦΒk → uIGηζs → ΟΜ1φaY → υgaΛΖ4 → ρaOΨΜ8 → ιyaΛnG → ΡaAνΜW → γkaΛΒM → ΕaGηΜi → ΟbLβΛY → ΕgYΝΖi → ePLβΨΙ → ΕxTΣoi → oM8οβy → ηΔ9ξiI → εΝKγZK → ΙΗcΙfe → WUQΦΣΡ → unjΒys → IB1φνη → υβΜZM4 → ρΔbΚi8 → ιYKγΞG → ΡΗeΗfW → kSQΦΥΓ → urHζus → Ν31φυa → υςbΚ64 → ρμXΞC8 → ιΩfΖOG → ΡzPΧmW → wkCλΒq → ΨH5ςηQ → νΞvpYC → αf5ςΗO → νΑQΦlC → αuEιrO → ΤΑ2υlU → σoEιx6 → νΤ8οTC → ηαowNI → ΝΒ7πka → ιcGηΚG → ΡΟWΟXW → kigΕΔΓ → OLHζγα → ΝΖzlga → cPDκΨΛ → ΦxXΞoS → sg8οΖu → ηP1φΨI → υΝwoZ4 → ρd7πΙ8 → κθUΡGF → ΤΠlzWU → ojDκΓy → ΦJ9ξεS → εΚrtcK → ΙX1φΟe → υhTΣΕ4 → ρoMαx8 → ιΓ8οjG → ηΡIεVI → ΝΛkΑba → cZFθΝΛ → ΡdXΞΙW → kgUΡΖΓ → mPHζΨΑ → ΝxDκoa → Φc8οΚS → ηsWΟtI → Νi0χΔa → χcKγΚ2 → υΗWΟf4 → ρiQΦΔ8 → ιuKγrG → ΡΗ2υfW → σkQΦΒ6 → νuGηrC → αΟ2υXO → σΑgΕl6 → νOEιΩC → αΤymTO → ΑpBμwm → αE6ρκO → λΥzlSE → ΦrDκuS → Φs2υtS → σs0χt6 → χν0χB2 → χυαM32 → υςΒj64 → ρμHζC8 → ιΩΜZOG → ΡzbΚmW → kYCλΞΓ → ΨfHζΗQ → ΝwQΦpa → uc6ρΚs → λX1φΟE → υΦgΕR4 → ρtNΩs8 → ιΑ0χlG → χΡEιV2 → υΤkΑT4 → ρpFθw8 → ιΡ6ρVG → λΡkΑVE → ΦlFθΑS → ΡsEιtW → Τk0χΒU → χoGηx2 → υΟ8οX4 → ρηgΕH8 → ιΞNΩYG → ΡΑeΗlW → kSEιΥΓ → ΤrHζuU → Νo2υxa → σc8οΚ6 → νηWΟHC → αΞhΔYO → ΑfLβΗm → ΕRDκΦi → ΦtLβsS → Εs0χti → χM0χβ2 → χυΓi32 → υςJδ64 → ρμΘdC8 → ιΩTΣOG → ΡznxmW → kD9ξλΓ → εΧHζQK → ΝΙuqda → cV3τΡΛ → ρlXΞΑ8 → ιgEιΖG → ΤΡOΨVU → yokΑxo → GA8οξι → ηδΠVKI → ΝΘjΒea → cTHζΤΛ → ΝpXΞwa → gc6ρΚΗ → λXPΧΟE → ΦwgΕpS → sO6ρΩu → λz1φmE → υΦCλR4 → ρΨssP8 → ιwψψoG → θxZΜoH → Οc8οΚY → ηgWΟΖI → ΝiOΨΔa → ycKγΚo → ΗX9ξΟg → εhPΧΕK → ΙwMαpe → ΓU6ρΣk → λnHζyE → ΦΝAνZS → γscΙtM → ΕW0χΠi → χjLβΓ2 → υΕIεh4 → ρΛMαb8 → ιΓYΝjG → ΡeIεΘW → ΛkSΤΒc → qYGηΞw → Οf5ςΗY → νgQΦΖC → αuOΨrO → Αy2υnm → σEAνκ6 → νγΤSLC → αΖpvgO → ΑP5ςΨm → νxDκoC → αΦ8οRO → ηΑsslI → ΝEψψιa → κΜJδaF → ΤΙaΛdU → oaUΡΜy → mb9ξΛΑ → εZDκΝK → ΦΙcΙdS → sWUΡΠu → mj1φΓΑ → υJDκε4 → ρΦΙcR8 → ιtVΠsG → Ρk0χΒW → χkGηΒ2 → υΟGηX4 → ρΟgΕX8 → ιhNΩΕG → ΡΑMαlW → ΓkEιΒk → ΤIGηζU → ΟΜnxaY → gb9ξΛΗ → εZPΧΝK → ΙwcΙpe → WU6ρΣΡ → λnjΒyE → ΦIAνζS → γΜrtaM → Εb1φΛi → υZLβΝ4 → ρΕcΙh8 → ιWMαΠG → ΡΓiΓjW → kKIεδΓ → ΛΘHζec → ΝYSΤΞa → qfbΚΗw → YR5ςΦΟ → νtfΖsC → αQ0χΧO → χΑuql2 → υF3τι4 → ςπΡU87 → λθlzGEΦΠDκWSΦsiΓtSsK0χδuχΘ1φe2φτSΤ43σπpv86νθ5ςGCναΟWNCαΒhΔkOΑMGηβmΟΔDκiYΦgKγΖSΗsOΨtgyQ0χΧoχv9ξq2υε4σJ4ροΙc98ιζVΠIGΡΜjΒaWkbHζΛΓΝZHζΝaΝdbΚΙacYUΡΞΛmfXΞΗΑgRDκΦΗΦtPΧsSws0χtqχ60χς2χυλC32υςΧP64ρμvpC8ιΩ5ςOGνΡymVCαlBμΑOαΑEιlOΤΑEιlUΤoEιxUΤo8οxUηo8οxIηΝ8οZIηΝcΙZIΝdVΠΙakcUΡΚΓmXHζΟΑΝhDκΕaΦcMαΚSΓsWΟtkiI0χζΕχΜLβa2υΕaΛh4ρaMαΜ8ιΓaΛjGΡaIεΜWΛkaΛΒcaYGηΞΝΟfbΚΗYgYQΦΞΗufPΧΗswR1φΦqυt5ςs4ρν0χB8χιαMF2υΣΒjU4ρnHζy8ιΝAνZGγΡcΙVMΕlVΠΑikMEιβΓΤΔHζiUΝoKγxaΗc8οΚgηXPΧΟIΝwgΕpacO6ρΩΛλzXΞmEΦgCλΖSΨsOΨtQyw0χpoχA6ρξ2υλγKD4ρΧΖfQ8ιvPΧqGΡw4σpWοk6ρΒAλεGηJEΦΟΙcXSshVΠΕukN1φαΓυΒHζk4ρΝGηZ8ιΟcΙXGΡhVΠΕWljMαΓΒΓJFθεkΡΚHζcWΝkWΟΒaicGηΚΕΟXLβΟYΕhfΖΕiQNLβαΨΕΒvpkiMH5ςηγνΞΔhYCαfLβΗOΕΑQΦliuMEιβsΤΔ1φiUυoKγx4ρΗ8οf8ιηQΦHGΡΞtrYWkf1φΗΓυRHζΦ4ρΝssZ8ιcψψΙGθΚNΩcHΟΑWΟlYigEιΖΕΤPLβΨUΕxnxoiMA8οξγηδΔhKIΝΘLβeaΕcSΤΚiqXLβΟwΕh5ςΕiνNLβαCαΕΑkhOΑNFθαmΡΒDκkWΦkGηΒSΟsGηtYΟg0χΖYχgOΨΖ2υyOΨn4ρyAνn8ιγAνLGγΡΕgVMΕlNΩΑiΑMEιβmΤΔDκiUΦoKγxSΗs8οtgηQ0χΧIχΝuqZ2υd3τΙ4ςπUΡ87λθlzGE