Base 102: 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
253 max steps20 → 1ο → ν3ι7αFΙVqnλ5εBΡNslγDΝRktΨHΕZezyfΓbmrη9ΦJΑdujΤLwhΛTgxΗXivΟPopο1ν3
353 max steps100 → 0ππ → οπ1 → ξπ2 → νπ3 → μπ4 → λπ5 → κπ6 → ιπ7 → θπ8 → ηπ9 → ζπA → επB → δπC → γπD → βπE → απF → ΩπG → ΨπH → ΧπI → ΦπJ → ΥπK → ΤπL → ΣπM → ΡπN → ΠπO → ΟπP → ΞπQ → ΝπR → ΜπS → ΛπT → ΚπU → ΙπV → ΘπW → ΗπX → ΖπY → ΕπZ → Δπa → Γπb → Βπc → Απd → zπe → yπf → xπg → wπh → vπi → uπj → tπk → sπl → rπm → qπn → pπo → oπpoπp
415 max stepsD00c → cCγΓ → ΟPΞQ → pmqp → 3ππν → ν2ν4 → λθ76 → εΩFCΡΘVOsbΒmQ5κΟεnpCΡ1ξOνrl4ι5κ8εΩFC
544 max steps30000 → 2πππξ → ξ1πξ3 → οκπ52 → ξιπ63 → νηπ84 → μδπB5 → λΩπF6 → κΤπK7 → ιΝπQ8 → θΖπX9 → ηxπfA → ζoπoB → εeπyC → δnπpD → γdπzE → βmπqF → αcπΑG → ΩlπrH → ΨbπΒI → ΧkπsJ → ΦaπΓK → ΥjπtL → ΤZπΔM → ΣiπuN → ΡYπΕO → ΠhπvP → ΟXπΖQ → ΞgπwR → ΝWπΗS → ΜfπxT → ΛVπΘU → ΚeπyV → ΙUπΙW → ΚbπΒV → ΙXπΖW → ΘaπΓX → ΗWπΗY → ΘXπΖX → ΗZπΔY → ΖWπΗZ → ΘWπΗX → ΘZπΔX → ΗXπΖYΗXπΖY
6685 max stepsF000ππ → ππEα01 → ποΚT11 → οξfx22 → νμHΧ44 → ιθΔZ88 → αΩTΚGG → ΙΘfxWW → cbHΧΓΓ → ΕRPΞΝa → olTΚsq → g71ξιy → νβHΧE4 → ιΜΔZS8 → αjTΚuG → ΙgAεxW → ΤcGΨΒM → ΗwOΟhY → qYEαΖo → ΛX1ξΗU → νgYΕx4 → ιWGΨΘ8 → αΗaΓXG → ΙZRΜΕW → kcUΙΒu → eP9ζΟΑ → ΦpLΣoK → Αw0οhe → οMEαΣ2 → νΛuiT4 → ιhBδw8 → αΡEαNG → ΛΙskVU → gd7θΑy → αNHΧΡG → ΙΕskZW → cV7θΙΓ → αdPΞΑG → ΙoMΡpW → uc0οΒk → οP9ζΟ2 → νΦooJ4 → ιΑππc8 → θΒVΘc9 → ΨcOΟΒI → ΕqOΟna → qU2νΚo → λf1ξy6 → νεIΦB4 → ιΣΒbM8 → αvPΞiG → ΙoCγpW → Οc0οΒQ → οoOΟp2 → νq0οn4 → οι2ν72 → νλαE54 → ιζΚTA8 → αΥfxKG → ΙzHΧeW → ΕcKΤΒa → yUOΟΚg → qfHΧyo → ΕJ1ξΦa → νΒTΚc4 → ιgOΟx8 → αqGΨnG → ΙΗ2νXW → λcYΕΒ6 → εWOΟΘC → ΡqaΓnO → sS2νΜm → λj5κu6 → ζδAεCB → ΥΣΟOML → yvpnig → ID1ξγΨ → νΞΔZQ4 → ιnTΚq8 → αg2νxG → λΙGΨV6 → εΗcΑXC → ΡZNΠΕO → trUΙml → e84λθΑ → ηΩLΣGA → ΦΘvhWK → ΑbDβΓe → ΝRLΣΝS → wljtsi → EA6ιζγ → γΥΜRKE → ΝzjteS → kL9ζΤu → Φx9ζgK → ΦΑGΨdK → ΗΑMΡdY → uYMΡΖk → uX9ζΗk → ΦZ9ζΕK → ΦΑUΙdK → ΑeMΡze → uMKΤΣk → yv9ζig → ΦICγΧK → ΟΔzdaQ → oTLΣΛq → wh1ξwi → νFDβα4 → ιΝΙUR8 → αldzsG → ΙM6ιΣW → γvbΒiE → ΝQCγΞS → ΟnjtqQ → oA2νζq → λΥ1ξK6 → νεyeB4 → ιΣJΥM8 → αΑuidG → ΙNBδΡW → ΡtbΒkO → sQ8ηΞm → Ψn5κqI → εΕ2νZC → λΡUΙN6 → εtdzkC → ΡM8ηΣO → ΨvrliI → ΕD5κγa → εΞTΚQC → ΡnfxqO → sI2νΧm → λΔ5κa6 → ζδSΛCB → ΤΠhvOM → wrDβmi → ΝE4λβS → ηΜjtSA → Φj9ζuK → ΦΑAεdK → ΤΑMΡdM → wuMΡji → uEAεβk → ΤΜ9ζSM → ΦwiuhK → ΑFBδαe → ΡΚLΣUO → wseyli → KE6ιβΦ → γΜzdSE → ΝjLΣuS → wkAεti → ΤE8ηβM → ΨΜvhSI → ΕjDβua → ΝUAεΚS → ΤkeytM → wK8ηΥi → ΨzDβeI → ΝΕKΤZS → ykUΙtg → eI8ηΧΑ → ΨΔLΣaI → ΕwSΛha → iUEαΚw → ΛfDβyU → ΝgIΦxS → ΓkGΨtc → ΗQ8ηΞY → ΨnXΖqI → ΕY2νΖa → λXTΚΗ6 → εgYΕxC → ΡWGΨΘO → ΗsaΓlY → YS6ιΜΗ → γjXΖuE → ΝYAεΖS → ΤkWΗtM → wa8ηΔi → ΨTDβΛI → ΝΕgwZS → kVFΩΙu → Ιd9ζΑW → ΦcMΡΒK → ΑuOΟje → qMAεΣo → Τv1ξiM → νwCγh4 → ιΟEαP8 → αΛooTG → ΙgππwW → ΘxBδgX → ΡaGΨΔO → ΗsSΛlY → iY6ιΖw → γXDβΗE → ΞΜYΕSR → mjVΘus → cB5κεΓ → εΣPΞMC → ΡvnpiO → sD1ξγm → νΞ5κQ4 → ιεmqB8 → αΣ3μMG → ιΙuiV8 → αdBδΑG → ΡΙMΡVO → uscΑlk → OA6ιζΡ → γΥrlKE → Νz5κeS → εkKΤtC → Ρy8ηfO → ΨsIΦlI → ΕΓ6ιba → γUQΝΚE → ΝmeyrS → kK4λΥu → ηz9ζeA → ΧΥKΤKJ → Γzxfec → QLHΧΤΟ → Εxnpga → UH1ξΨΛ → νΖfxY4 → ιXHΧΗ8 → αΕYΕZG → ΙWUΙΘW → ecaΓΒΑ → SPLΣΟΝ → wpjtoi → EA0οζγ → οΥΜRK2 → νzjte4 → ιL9ζΤ8 → αΦwgJG → ΙΒFΩcW → ΙcOΟΒW → qcOΟΒo → qP1ξΟo → νp1ξo4 → νι0ο74 → οιαE72 → νβΚTE4 → ιΜfxS8 → αjHΧuG → ΙΕAεZW → ΤcUΙΒM → weOΟzi → qLDβΤo → Νx1ξgS → νkGΨt4 → ιΗ8ηX8 → αΨYΕHG → ΙΖVΘYW → dbWΗΓΒ → aRNΠΝΕ → slTΚsm → g75κιy → εβHΧEC → ΡΜΔZSO → sjTΚum → gB5κεy → εΣHΧMC → ΡΕuiZO → sVBδΙm → Ρd5κΑO → εsMΡlC → Ρu6ιjO → γsAεlE → ΤΝ6ιRM → γwkshE → ΝF7θαS → αΚjtUG → Ιf9ζyW → ΦcIΦΒK → ΓΑOΟdc → qQMΡΞo → un1ξqk → νA2νζ4 → λιΤK76 → εβxfEC → ΡΜHΧSO → Εsiula → UC6ιδΛ → γΠfxOE → ΝrHΧmS → Εk4λta → ηU8ηΚA → ΨΦeyJI → ΕΒJΥca → ΑUOΟΚe → qfLΣyo → wJ1ξΦi → νΒDβc4 → ιΝOΟR8 → αqksnG → Ι82νθW → λΩbΒG6 → εΘPΞWC → ΡoaΓpO → sS0οΜm → οj5κu2 → νεAεB4 → ιΤΡML8 → αxtjgG → ΙH9ζΨW → ΦΖbΒYK → ΑXPΞΗe → oZLΣΕq → wV1ξΙi → νdDβΑ4 → ιΝMΡR8 → αuksjG → ΙB7θεW → αΣbΒMG → ΙvPΞiW → ocCγΒq → ΟP1ξΟQ → νpnpo4 → ι20οξ8 → ομΩF42 → νθΘV84 → ιΩbΒG8 → αΘPΞWG → ΙoaΓpW → cS0οΜΓ → οjPΞu2 → νoAεp4 → ιΤ0οL8 → οαwgF2 → νΚFΩU4 → ιΙeyV8 → αdJΥΑG → ΙΑMΡdW → ucMΡΒk → uP9ζΟk → Φp9ζoK → ΦΑ0οdK → οΑMΡd2 → νuMΡj4 → ιuAεj8 → αΤAεLG → ΤΙwgVM → wdFΩΑi → ΙNDβΡW → ΝtbΒkS → kQ8ηΞu → Ψn9ζqI → ΦΕ2νZK → λΑUΙd6 → εeMΡzC → ΡuKΤjO → ysAεlg → ΤI6ιΧM → γΔvhaE → ΝTDβΛS → ΝkgwtS → kG8ηΩu → ΨΘ9ζWI → ΦΕaΓZK → ΑVRΜΙe → kdLΣΑu → wN9ζΡi → ΦtDβkK → ΝΑ8ηdS → ΨkMΡtI → Εu8ηja → ΨUAεΚI → ΤΕeyZM → wVJΥΙi → ΑdDβΑe → ΝNLΣΡS → wtjtki → EA8ηζγ → ΨΥΜRKI → Εzjtea → UL9ζΤΛ → ΦxfxgK → ΑIGΨΧe → ΗΔLΣaY → wYSΛΖi → iXDβΗw → ΝZDβΕS → ΝkUΙtS → ke8ηzu → ΨL9ζΤI → ΦΕwgZK → ΑVFΩΙe → ΙdLΣΑW → wcMΡΒi → uPDβΟk → Νp9ζoS → Φk0οtK → οΑ8ηd2 → νΨMΡH4 → ιΖtjY8 → αX9ζΗG → ΦΙYΕVK → ΑdVΘΑe → cNLΣΡΓ → wtPΞki → oE8ηβq → ΨΜ1ξSI → νΕiuZ4 → ιVBδΙ8 → αΡcΑNG → ΙtNΠkW → sc8ηΒm → ΨP5κΟI → εΕooZC → ΡUππΙO → ΠΚ7θUP → αqeynG → ΙK2νΥW → λzbΒe6 → εQKΤΞC → ΡymqfO → sJ3μΦm → ιΒ5κc8 → εαOΟFC → ΡΚpnUO → sf1ξym → νJ5κΦ4 → ιεΑcB8 → αΣNΠMG → ΙvrliW → cD5κγΓ → εΞPΞQC → ΡomqpO → s40ομm → οθ5κ82 → νεΨGB4 → ιΣΖXM8 → αvXΖiG → ΙYCγΖW → ΟcWΗΒQ → oaOΟΔq → qT1ξΛo → νh1ξw4 → νιEα74 → ιβΚTE8 → αΜfxSG → ΙjHΧuW → ΕcAεΒa → ΤUOΟΚM → wqeyni → KE2νβΦ → λΜzdS6 → εjLΣuC → ΡwAεhO → ΤsEαlM → Λw6ιhU → γgEαxE → ΝΛGΨTS → ΗkgwtY → YG8ηΩΗ → ΨΘXΖWI → ΕbXΖΓa → YUQΝΚΗ → mfXΖys → YJ5κΦΗ → εΒXΖcC → ΡYOΟΖO → sqWΗnm → a62νκΕ → λδTΚC6 → εΠfxOC → ΡrHΧmO → Εs4λla → ηU6ιΚA → γΦeyJE → ΝΒJΥcS → ΑkOΟte → qM8ηΣo → Ψv1ξiI → νΕCγZ4 → ιΟUΙP8 → αpdzoG → ΙM0οΣW → οvbΒi2 → νQCγΞ4 → ιΟmqP8 → αp3μoG → ιΙ0οV8 → οαcΑF2 → νΚNΠU4 → ιseyl8 → αK6ιΥG → γΙyeVE → ΝdJΥΑS → ΑkMΡte → uM8ηΣk → Ψv9ζiI → ΦΕCγZK → ΟΑUΙdQ → oeMΡzq → uL1ξΤk → νx9ζg4 → ιΦGΨJ8 → αΗΑcXG → ΙZNΠΕW → scUΙΒm → eP5κΟΑ → εpLΣoC → Ρw0οhO → οsEαl2 → νΛ6ιT4 → ιγgwD8 → αΞFΩQG → ΚΘmqWV → eb3μΓΑ → ιRLΣΝ8 → αwkshG → ΙF7θαW → αΚbΒUG → ΙfPΞyW → ocIΦΒq → ΓP1ξΟc → νpPΞo4 → ιo0οp8 → οα0οF2 → ονΙU32 → νκdz64 → ιδLΣC8 → αΠvhOG → ΙrDβmW → Νc4λΒS → ηkOΟtA → Φq8ηnK → ΨΑ2νdI → λΕMΡZ6 → εuUΙjC → ΡeAεzO → ΤsKΤlM → yw6ιhg → γIEαΧE → ΝΛΓaTS → khRΜwu → kF9ζαu → ΦΚ9ζUK → ΦΑeydK → ΑNJΥΡe → ΑtLΣke → wM8ηΣi → ΨvDβiI → ΝΕCγZS → ΟkUΙtQ → oe8ηzq → ΨL1ξΤI → νΕwgZ4 → ιVFΩΙ8 → αΙcΑVG → ΙdNΠΑW → scMΡΒm → uP5κΟk → εp9ζoC → ΦΡ0οNK → οΑskd2 → νN7θΡ4 → ιαskF8 → αΚ7θUG → αΙeyVG → ΙdJΥΑW → ΑcMΡΒe → uPLΣΟk → wp9ζoi → ΦE0οβK → οΜzdS2 → νjLΣu4 → ιwAεh8 → αΤEαLG → ΛΙwgVU → gdFΩΑy → ΙNHΧΡW → ΕtbΒka → UQ8ηΞΛ → ΨnfxqI → ΕI2νΧa → λΔTΚa6 → εgSΛxC → ΡiGΨvO → ΗsCγlY → ΟY6ιΖQ → γoWΗpE → Νa0οΔS → οkSΛt2 → νi8ηv4 → ιΨCγH8 → αΟΕYPG → ΙpVΘoW → db0οΓΒ → οRNΠΝ2 → νsksl4 → ι86ιθ8 → γαΨGFE → ΝΚΖXUS → kfXΖyu → YJ9ζΦΗ → ΦΒXΖcK → ΑYOΟΖe → qXLΣΗo → wZ1ξΕi → νVDβΙ4 → ιΝcΑR8 → αlNΠsG → Ιs6ιlW → γc6ιΒE → γΝOΟRE → ΝqksnS → k82νθu → λΩ9ζG6 → εΦΗWJC → ΡΒZΔcO → sUOΟΚm → qf5κyo → εJ1ξΦC → νΡΑcN4 → ιtNΠk8 → αs8ηlG → ΨΙ6ιVI → γΕcΑZE → ΝVNΠΙS → skcΑtm → O95κηΡ → εΧrlIC → ΡΔ5κaO → εsSΛlC → Ρi6ιvO → γsCγlE → ΟΝ6ιRQ → γokspE → Ν80οθS → οΩjtG2 → νΘ9ζW4 → ιΦaΓJ8 → αΒRΜcGΙkOΟtWqc8ηΒoΨP1ξΟIνΕooZ4ιUππΙ8θΚNΠU9ΨseylIΕK6ιΥaγzTΚeEΝgKΤxSykGΨtgΗI8ηΧYΨΔXΖaIΕYSΛΖaiXTΚΗwgZDβΕyΝVHΧΙSΕkcΑtaUO8ηΠΛΨrfxmIΕI4λΧaηΔTΚaAΦgSΛxKΑiGΨveΗMCγΣYΟvXΖiQoYCγΖqΟX1ξΗQνoYΕp4ιW0οΘ8οαaΓF2νΚRΜU4ιkeyt8αK8ηΥGΨΙyeVIΕdJΥΑaΑUMΡΚeufLΣykwJ9ζΦiΦΒDβcKΝΑOΟdSqkMΡtou91ξηkνΧ9ζI4ιΦΓaJ8αΒRΜcG