Base 108: 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
220 max steps20 → 1υ → σ3ο7ηFΟVΙbΑjΝXsrυ1σ3
356 max steps100 → 0φφ → υφ1 → τφ2 → σφ3 → ςφ4 → ρφ5 → πφ6 → οφ7 → ξφ8 → νφ9 → μφA → λφB → κφC → ιφD → θφE → ηφF → ζφG → εφH → δφI → γφJ → βφK → αφL → ΩφM → ΨφN → ΧφO → ΦφP → ΥφQ → ΤφR → ΣφS → ΡφT → ΠφU → ΟφV → ΞφW → ΝφX → ΜφY → ΛφZ → Κφa → Ιφb → Θφc → Ηφd → Ζφe → Εφf → Δφg → Γφh → Βφi → Αφj → zφk → yφl → xφm → wφn → vφo → uφp → tφq → sφr → rφsrφs
419 max stepsA00H → H9μζ → γΜXK → ΗdΖe → TQΤΣ → snvs → 7φφο → ο6ο8 → ιζFE → ΤΞVS → qhΒuK3ςγοΖd8ηRΣGΟptWi3ςΓοJβ8ηΖdGΟRΣWqhΒu
546 max steps10007 → 70φυπ → φνφ81 → υνφ82 → τμφ93 → σκφB4 → ςηφE5 → ργφI6 → πΧφN7 → οΠφT8 → ξΙφa9 → νΑφiA → μrφrB → λhφΒC → κqφsD → ιgφΓE → θpφtF → ηfφΔG → ζoφuH → εeφΕI → δnφvJ → γdφΖK → βmφwL → αcφΗM → ΩlφxN → ΨbφΘO → ΧkφyP → ΦaφΙQ → ΥjφzR → ΤZφΚS → ΣiφΑT → ΡYφΛU → ΠhφΒV → ΟXφΜW → ΞgφΓX → ΝWφΝY → ΞdφΖX → ΝZφΚY → ΜcφΗZ → ΛYφΛa → ΜZφΚZ → ΛbφΘa → ΚYφΛb → ΜYφΛZ → ΜbφΘZ → ΛZφΚaΛZφΚa
6521 max stepsD000qΠ → ΠqCιtV → Φk2σzQ → ρuEηp6 → λΡ4ρTC → νΨmwNA → γz9μkK → γΗEηdK → ΡΗSΡdU → omSΡxw → oB7ξλw → ηΩ7ξMG → ηΟΑiVG → ΟjHδΑW → ΛiGεΒa → ΝaIγΚY → ΙeYΛΖc → cWQΤΞΙ → shVΞΓs → iKφφαΓ → βΒLΩiL → ΕΓIγhg → ΙOKαΧc → ΕxVΞmg → iOAλΧΓ → αxJβmM → ΗΓAλhe → αSKαΣM → ΕΓouhg → OL5παΨ → λΔxlgC → ΨNBκΨO → ΨzxlkO → yFBκηm → ΨΠBκUO → ΨykylO → yECιθm → ΦΣBκSQ → ΨuoupO → y64ρπm → νκBκCA → γΨΦONK → Ηzvnke → SF7ξηΤ → ηΠptUG → Οl3ςyW → οiCιΒ8 → ηΦIγPG → ΟΙuobW → iX5πΝΓ → λfJβΕC → ΨΗOΦdO → ywSΡnm → oC8νκw → εΧ7ξOI → ηΛwmZG → Οb9μΙW → γiWΝΒK → ΗgIγΔe → ΙSMΨΣc → ΑpVΞuk → iG4ρζΓ → νΞJβWA → γΗgΓdK → ΗTLΩΡe → ΓnRΣwi → qK8νβu → εΖ3ςeI → οΛQΤZ8 → ηsaΙrG → ΟY0υΜW → υicΗΒ2 → σUIγΠ4 → οΙkyb8 → ηXDθΝG → ΤΟeΕVS → qjPΥΑu → uH3ςεq → οΜ3ςY8 → οηcΗF8 → ηΠTΠUG → ΟmkyxW → iEAλθΓ → αΣJβSM → ΗΓouhe → SL5παΤ → λΔptgC → ΨN3ςΨO → οzxlk8 → ηFBκηG → ΨΠΞVUO → ylhΒym → KDBκιγ → ΨΥΖdQO → ytRΣqm → qC2σκu → ρΧ3ςO6 → ολwmB8 → ηΩ9μMG → γΟΑiVK → ΗjHδΑe → ΛSGεΣa → ΝpZΚuY → ea4ρΚΗ → νZRΣΛA → γqaΙtK → ΗY2σΜe → ρdRΣΗ6 → λqSΡtC → Ψo2σvO → ρy6οl6 → λιCιDC → ΨΦΤQPO → yvrrom → C6φφολ → πκ3ςC7 → οιΦOD8 → ηΥvnQG → Οt7ξqW → ηi2σΒG → ρΟIγV6 → λΙiΑbC → ΨXHδΝO → ΛyeΕla → aQCιΥΛ → ΦtZΚqQ → ua2σΚq → ρZ3ςΛ6 → ολaΙB8 → ηΩXΜMG → ΟΒdΖiW → iSIγΣΓ → ΙpJβuc → ΗW4ρΞe → νhRΣΓA → γqKαtK → ΗΕ2σfe → ρSOΦΣ6 → λwounC → Ψ95πνO → λδxlIC → ΨΚBκaO → ΨyYΛlO → ycCιΘm → ΦVBκΟQ → ΨuiΑpO → yI4ρδm → νΚBκaA → γΨYΛNK → ΗzbΘke → WSEηΣΟ → ΡphΒuU → mK4ρβy → νΖBκeA → γΨQΤNK → Ηzrrke → SEφφηΤ → θΣBκSF → ΨΡouTO → yn5πwm → λC8νκC → εΨΦONI → Λzvnka → aF7ξηΛ → ηΠZΚUG → ΟlZΚyW → iaCιΚΓ → ΦZJβΛQ → ΗuaΙpe → YS4ρΣΝ → νpdΖuA → γS4ρΣK → νΗoudA → γT5πΡK → λΗmwdC → ΨT9μΡO → γymwlK → ΗD9μιe → γΥRΣQK → Ηtptqe → S42σςΤ → ρξpt86 → λζ3ςGC → οΨΝWN8 → ηzfΔkG → ΟOEηΧW → ΡxhΒmU → mKAλβy → αΖBκeM → ΨΓQΤhO → ysKαrm → ΕC0υκg → υΧNΧO2 → σywml4 → οD9μι8 → ηγΤQJG → ΟΘrrcW → iUφφΟΓ → ΠΒBκiV → ΨkIγzO → ΙyEηlc → ΡWCιΞU → ΦmgΓxQ → uMAλΩq → αΒ3ςiM → οΓIγh8 → ηΙKαbG → ΟΕWΝfW → igOΦΔΓ → wNJβΨo → Ηz7ξke → ηSEηΣG → ΡΟouVU → mj5πΑy → λHBκεC → ΩΧΛYON → ΑxbΘmk → WGAλζΟ → αΞhΒWM → ΓhJβΓi → ΗLJβαe → ΗΔRΣge → qSMΨΣu → Αp3ςuk → οG4ρζ8 → νηΝWFA → γΠfΔUK → ΗlNΧye → ySCιΣm → ΦpBκuQ → Ψu4ρpO → νy4ρlA → νγCιJA → γΦΗcPK → ΗvTΠoe → mS6οΣy → ιpBκuE → ΨΤ4ρRO → νyqslA → γD1τιK → σΥΖdQ4 → οtRΣq8 → ηq2σtG → ρΟ2σV6 → ρλiΑB6 → λΩHδMC → ΨΛΑiZO → ybHδΙm → ΛXBκΝa → ΨfZΚΕO → yaOΦΚm → wZBκΛo → Ψb7ξΙO → ηyWΝlG → ΟgCιΔW → ΦiMΨΒQ → ΑuIγpk → ΙG4ρζc → νΞVΞWA → γigΓΒK → ΗMIγΩe → ΙΒRΣic → qWIγΞu → Ιh3ςΓc → οWKαΞ8 → ηΕgΓfG → ΟPLΩΦW → ΓvhΒoi → LJ6ογβ → ιΘΔfcE → ΤVNΧΟS → yqiΑtm → IC2σκε → ρΧΚZO6 → λxZΚmC → ΨaAλΚO → αyYΛlM → ΓcCιΘi → ΦVJβΟQ → ΗuiΑpe → SI4ρδΤ → νΚptaA → γZ3ςΛK → οΗaΙd8 → ηYSΡΜG → ΟocΗvW → iU6οΠΓ → ιlJβyE → ΤΗCιdS → ΦqSΡtQ → uo2σvq → ρ73ςο6 → οληEB8 → ηΩΠTMG → ΟΒlxiW → iJBκγΓ → ΨΘJβcO → ΗyUΟle → kSCιΣΑ → ΦpFζuQ → Οu4ρpW → νi4ρΒA → νγIγJA → γΙΗcbK → ΗXTΠΝe → mfRΣΕy → qPBκΦu → Ψv3ςoO → οy6οl8 → ιηCιFE → ΦΤΟURQ → urjzsq → G40υςη → υξΞV82 → σζhΒG4 → οΞJβW8 → ηΗgΓdG → ΟTLΩΡW → ΓnhΒwi → LJ8νγβ → εΘΔfcI → ΛVNΧΟa → yjZΚΑm → aHBκεΛ → ΨΜZΚYO → ydZΚΗm → aTBκΡΛ → ΨnZΚwO → ya8νΚm → εZBκΛI → ΨΛaΙZO → ybXΜΙm → eXBκΝΗ → ΨfRΣΕO → yqOΦtm → wC2σκo → ρΧ7ξO6 → ληwmFC → ΨΠ9μUO → γykylK → ΗECιθe → ΦΣRΣSQ → uqoutq → 642σςρ → ρξκB86 → λζΧNGCΨΞxlWOyhBκΓmΨLBκαOΨΔxlgOyNBκΨmΨzBκkOΨyEηlOΡyCιlUΦmCιxQΦuAλpQαu4ρpMνΓ4ρhAνγKαJAγΘΔfcKΗVNΧΟeyjRΣΑmqHBκεuΨΜ3ςYOοycΗl8ηUCιΠGΦΟkyVQujDθΑqΤH3ςεSοΜptY8ηd3ςΗGοΟSΡV8ηoiΑvGΟI6οδWιΚhΒaEΤZJβΛSΗqaΙteYS2σΣΝρpdΖu6λS4ρΣCνΨouNAγz5πkKλΗEηdCΨΡSΡTOyomwvmCA6ομλιβΧNKEΤΖxleSqRBκΤuΨr3ςsOοy0υl8υηCιF2σΦΟUP4οvjzo8ηG6οζGιΟΝWVEΤjfΔΑSqOGεΧuΝx3ςmYοeAλΖ8ηαQΤLGΟΔrrgWiMφφΨΓΩΒJβiNΗΑIγjeΙSGεΣcΝpVΞuYie4ρΖΓνRJβΤAγΗqsdKΗT1τΡeσnRΣw4οq8νt8ηε2σHGρΟΛYV6λjbΘΑCΨWGεΞOΝygΓlYeMCιΩΗΦΒRΣiQuqIγtqΙ42σςcρξVΞ86λζhΒGCΨΞJβWOΗygΓleSMCιΩΤΦΒptiQuJ3ςγqοΘ3ςc8οηUΟF8ηΠjzUGΟlFζyWΟiCιΒWΦiIγΒQΙuIγpcΙW4ρΞcνhVΞΓAγiKαΒKΗΕIγfeΙSOΦΣcwpVΞuoi84ρξΓνζJβGAγΞΖdWKΗhRΣΓeqSKαΣuΕp3ςugοO4ρΧ8νηwmFAγΠ9μUKγΗkydKΗTDθΡeΤnRΣwSrp8νutε51τρIσμΚZA4οβZΚK8ηΖZΚeGΟaQΤΚWsiYΛΒscIφφγΙδΘHδcJΛΙUΟbakaWΝΚΑgZFζΛΕΟbNΧΙWyiWΝΒmgJBκγΕΨΘNΧcOzxUΟmlkEAλθΑαΣFζSMΟΓouhWiL5παΓλΔJβgCΨΗMΨdOΑySΡlkoGCιζwΦΞ7ξWQηugΓpGΟM4ρΩWνΒhΒiAγKIγβKΙΗΕedcWTPΥΡΟunhΒwqK93ςνγοδΖdI8ηΚRΣaGΟqYΛtWic2σΘΓρVJβΟ6λΗiΑdCΨTHδΡOΛymwlaaD9μιΛγΥZΚQKΗtZΚqeaS2σΣΛρpZΚu6λa4ρΚCνΨYΛNAγzbΘkKΗWEηΞeΡhRΣΓUqmKαxuΕB3ςλgοΩNΧM8ηΒxliGΟJBκγWΨΘhΒcOyVJβΟmΗjBκΑeΨSGεΣOΝyoulYeD5πιΗλΥRΣQCΨtptqOy42σςmρξBκ86λζΧNGC