Base 120: Maximum Iteration Sequences: Full Cycle

Blog: The First Pixel: Kaprekar's Constant 6174

Radix Character Encoding
0123456789ABCDEF
GHIJKLMNOPQRSTUV
WXYZabcdefghijkl
mnopqrstuvwxyzΑΒ
ΓΔΕΖΗΘΙΚΛΜΝΞΟΠΡΣ
ΤΥΦΧΨΩαβγδεζηθικ
λμνξοπρςστυφχψωА
БВГДЕЖЗИЙКЛМНОПР

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
257 max steps20 → 1З → Е3Б7σFγVυDηRΓtρHΨZΝjΑvω9οJΤdΦbwzГ5χBλNΛlΙnΡfΕrιPΗpαXεTyxЗ1Е3
362 max steps100 → 0ИИ → ЗИ1 → ЖИ2 → ЕИ3 → ДИ4 → ГИ5 → ВИ6 → БИ7 → АИ8 → ωИ9 → ψИA → χИB → φИC → υИD → τИE → σИF → ςИG → ρИH → πИI → οИJ → ξИK → νИL → μИM → λИN → κИO → ιИP → θИQ → ηИR → ζИS → εИT → δИU → γИV → βИW → αИX → ΩИY → ΨИZ → ΧИa → ΦИb → ΥИc → ΤИd → ΣИe → ΡИf → ΠИg → ΟИh → ΞИi → ΝИj → ΜИk → ΛИl → ΚИm → ΙИn → ΘИo → ΗИp → ΖИq → ΕИr → ΔИs → ΓИt → ΒИu → ΑИv → zИw → yИx → xИyxИy
425 max steps100E → E0Зυ → ЗζR2 → ЕΒt4 → Б7А8 → τρGF → εΩXU → ypΖy → FИИσ → σEσG → εβVU → ytΒy → 7ИИБ → Б6Б8 → υςFE → ηβVS → ΓtΒu → 96БА → υπHE → ηΧZS → ΓlΚu → O7АλσΚlGγNκWΛtΒmO7Аλ
550 max steps1000D → D0ИЗφ → ИσИE1 → ЗσИE2 → ЖςИF3 → ЕπИH4 → ДνИK5 → ГιИO6 → ВδИT7 → БΧИZ8 → АΟИg9 → ωΗИoA → ψxИxB → χnИΘC → φwИyD → υmИΙE → τvИzF → σlИΚG → ςuИΑH → ρkИΛI → πtИΒJ → οjИΜK → ξsИΓL → νiИΝM → μrИΔN → λhИΞO → κqИΕP → ιgИΟQ → θpИΖR → ηfИΠS → ζoИΗT → εeИΡU → δnИΘV → γdИΣW → βmИΙX → αcИΤY → ΩlИΚZ → ΨbИΥa → ΧkИΛb → ΦaИΦc → ΧhИΞb → ΦdИΣc → ΥgИΟd → ΤcИΤe → ΥdИΣd → ΤfИΠe → ΣcИΤf → ΥcИΤd → ΥfИΠd → ΤdИΣeΤdИΣe
6377 max steps60000L → L5ИИВξ → ГνDτL6 → χηΟgRC → λΔXΩsO → ΛqAχΖm → νOEσκM → εΟΙmhU → yXLμαy → ΟqИИΕi → ΞΖ9ψqj → οUEσδK → εΤwydU → yf1ЖΡy → ЕaИИΦ4 → ДΧXΩa5 → ωqkΛΖA → οQEσθK → εΤΕqdU → yfDτΡy → ηaИИΦS → ζΧ9ψaT → οΑkΛvK → ΤQ4Гθe → ωΖdΣqA → οeEσΣK → εΤcΤdU → ygeΡΠy → cYИИΨΦ → ΩΥ1ЖcZ → ЕogΟΘ4 → БYIοΩ8 → σΦoΗbG → γjHπΝW → ΨuSεΒa → Αm6БΚw → υN3ДλE → БηΛkR8 → σΔPθsG → γΗAχpW → νuGρΒM → αΟ6БhY → υqWαΖE → ηsEσΔS → εΓAχtU → νy8ωxM → ρΟ0ЗhI → ЗΨWαZ2 → ЕsmΙΔ4 → БMAχμ8 → σνΝiLG → γΠTδgW → yuYΨΒy → o6ИИБΙ → ВΘfΠo7 → υaIοΧE → ηΦkΛbS → ΓjPθΝu → ΗT7Аεq → σzFςwG → δβ2ЕWV → ГwsΓz6 → χA2ЕψC → ГξκNK6 → χΣΚleC → λdNκΤO → ΜΚeΡml → cQMλθΦ → ΝΖhΞqk → WSEσζγ → εΒtΒuU → y86БАy → υρИИGE → τς3ДGF → БεαWT8 → σzrΔwG → γC2ЕφW → ГκtΒO6 → χΚ7АmC → σλMλNG → γΝΛkjW → uTPθεΓ → Ηz7Аwq → σG2ЕςG → ГγαWV6 → χvrΔΑC → λC4ГφO → ωκΚlOA → οΚNκmK → ΤΛMλle → ΝeOιΣk → ΙdRζΤo → ΓfJξΡu → Τb7АΦe → σjdΣΝG → γeSεΣW → ΑucΤΒw → g73ДБΡ → БτZΧE8 → σζlΚSG → γΒNκuW → Λu6БΒm → υO6БκE → υηΙmRE → ηΔLμsS → ΟΓAχti → νW8ωβM → ρΟsΓhI → ΨX9ψαa → οrlΚΕK → ΤOCυκe → ιΚdΣmQ → ΗeMλΣq → ΝdFςΤk → γfRζΡW → ΓuaΦΒu → k86БАΝ → υςRζGE → ηβΒtWS → Γt7АΓu → σ97АωG → σπβVIG → γΧtΒaW → ul7АΛΓ → σP7АιG → σγΗoVG → γvHπΑW → Ψu4ГΒa → ωm6БΚA → υοMλJE → ηΥΜjcS → ΓhRζΟu → ΓX7Аαu → σr7АΕG → σγCυVG → ιγuΑVQ → Ηv5ВΑq → χG4ГςC → ωλαWNA → οΜrΔkK → ΤRBφηe → λΔdΣsO → ΛeAχΣm → νdNκΤM → ΟΛeΡli → cWOιβΦ → ΙthΞΓo → WK8ωξγ → ρΣtΒeI → Ψd7АΤa → σmeΡΚG → γcMλΥW → ΝugΟΒk → YS6Бζα → υΒpΖuE → ηG6БςS → υβΒtWE → ηt7АΓS → σΓ8ωtG → ργ8ωVI → ρΨuΑZI → Ψn5ВΙa → χmKνΚC → λΡMλfO → ΝΛaΦlk → kSOιζΝ → ΙΒRζuo → ΓK6Бξu → υΣ7АeE → σηcΤRG → γΔfΠsW → uaAχΧΓ → νl7АΛM → σΟOιhG → γΙWαnW → usKνΔΓ → ΡB7Аχg → σμZΧMG → γΞlΚiW → uVNκγΓ → Λv7АΑm → σO4ГκG → ωγΙmVA → οvLμΑK → ΤΟ4Гhe → ωeWαΣA → οscΤΔK → ΤgAχΠe → νeYΨΣM → ΟocΤΘi → gWIοβΡ → ΦtZΧΓc → mi8ωΞΛ → ρVNκγI → ΨΛuΑla → mP5ВιΛ → χΘNκoC → λΛIοlO → ΦΛOιlc → ΙiOιΞo → ΙVJξγo → ΤvJξΑe → Τe4ГΣe → ωecΤΣA → οgcΤΠK → ΤgYΨΠe → oeYΨΣΙ → odJξΤΙ → ΤfJξΡe → ΤeaΦΣe → kecΤΣΝ → gdRζΤΡ → ΓfZΧΡu → mb7АΦΛ → σjNκΝG → γΛSεlW → ΑuOιΒw → Ι73ДБo → БτJξE8 → σζΣdSG → γΒdΣuW → ue6БΣΓ → υd7АΤE → σηeΡRG → γΔbΥsW → uiAχΞΓ → νV7АγM → σΟuΑhG → γX5ВαW → χuqΕΒC → λE6БτO → υζΚlSE → ηΒNκuS → ΛΓ6Бtm → υO8ωκE → ρηΙmRI → ΨΔLμsa → ΟmAχΚi → νWMλβM → ΟΝsΓji → WT9ψεγ → οztΒwK → Τ82ЕАe → ГςdΣG6 → χβdΣWC → λtdΣΓO → Λe8ωΣm → ρdNκΤI → ΨΛeΡla → mcOιΥΛ → ΙhNκΟo → ΛXJξαm → ΤrNκΕe → ΛeCυΣm → ιdNκΤQ → ΛΗeΡpm → cOGρκΦ → αΚhΞmY → qWMλβΗ → ΝtFςΓk → γS8ωζW → ρΒtΒuI → Ψ86БАa → υςlΚGE → ηβNκWS → ΛΓsΓtm → OA8ωψλ → ρξΚlKI → ΨΣNκea → ΛmcΤΚm → gOMλκΡ → ΝΚZΧmk → mSMλζΛ → ΝΒNκuk → ΛS6Бζm → υΒNκuE → ηΛ6БlS → υΓOιtE → ηΙ8ωnS → ρΓKνtI → ΨΡ8ωfa → ρmaΦΚI → ΨkMλΜa → ΝmQηΚk → ΕSMλζs → ΝΒBφuk → λS6БζO → υΛΑulE → ηP5ВιS → χΘΒtoC → λJ7АοO → σΥΚlcG → γhNκΟW → ΛuWαΒm → sO6БκΕ → υΚBφmE → ληMλRO → ΝΛΓslk → SP9ψιη → οΘΒtoK → ΤJ7Аοe → σΥdΣcG → γhdΣΟW → ueWαΣΓ → sd7АΤΕ → σfBφΡG → λγaΦVO → ΛvjΜΑm → SO4Гκη → ωΚΒtmA → οN7АλK → σΤΛkdG → γfPθΡW → ΗuaΦΒq → kG6БςΝ → υβRζWE → ηΓsΓtS → ΓA8ωψu → ρξ7АKI → σΨΡeZG → γnbΥΙW → uiKνΞΓ → ΡV7Аγg → σvZΧΑG → γm4ГΚW → ωuMλΒA → οΝ6БjK → υΤSεdE → ηΑeΡvS → Γc4ГΥu → ωh7АΟA → σοWαJG → γΥrΔcW → uhBφΟΓ → λX7АαO → σΛqΕlG → γPDτιW → ηΘtΒoS → ΓJ7Аοu → σΥ7АcG → σγgΟVG → γvXΩΑW → uq4ГΖΓ → ωF7АσA → σογUJG → γΥvzcW → uh3ДΟΓ → БX7Аα8 → τςqΕGF → εβDτWU → ηysΓxS → ΓA0Зψu → Зξ7АK2 → ЕσΡeF4 → БδbΥU8σxhΞyGγW0ЗβWЗusΓΒ2ЕA6Бψ4БυνKD8σθΠfQGγΖZΧqWumEσΚΓεN7АλUσΜxxkGγQИИηWθβ3ДWRБΕsΓr8σD9ψυGοθβVQKΤΖtΒqeeF7АσΤσδdΣUGγxdΣyWue0ЗΣΓЗd7АΤ2ЕσeΡF4БδbΥU8