Base 117: Maximum Iteration Sequences: Cycle Start

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
Cycle Start
11 max steps10
23 max steps10 → 0Е → Д1 → В3
359 max steps100 → 0ЕЕ → ДЕ1 → ГЕ2 → ВЕ3 → БЕ4 → АЕ5 → ωЕ6 → ψЕ7 → χЕ8 → φЕ9 → υЕA → τЕB → σЕC → ςЕD → ρЕE → πЕF → οЕG → ξЕH → νЕI → μЕJ → λЕK → κЕL → ιЕM → θЕN → ηЕO → ζЕP → εЕQ → δЕR → γЕS → βЕT → αЕU → ΩЕV → ΨЕW → ΧЕX → ΦЕY → ΥЕZ → ΤЕa → ΣЕb → ΡЕc → ΠЕd → ΟЕe → ΞЕf → ΝЕg → ΜЕh → ΛЕi → ΚЕj → ΙЕk → ΘЕl → ΗЕm → ΖЕn → ΕЕo → ΔЕp → ΓЕq → ΒЕr → ΑЕs → zЕt → yЕu → xЕv → wЕw
44 max stepsx000 → wЕЕw → wvwx → 1ЕЕД → Д0Д2
550 max steps10000 → 0ЕЕЕЕ → ДЕЕЕ1 → Д0ЕД2 → ЕБЕ31 → ДБЕ32 → ГАЕ43 → ВψЕ64 → БυЕ95 → АρЕD6 → ωμЕI7 → ψζЕO8 → χΨЕV9 → φΟЕdA → υΖЕmB → τvЕwC → σlЕΗD → ςuЕxE → ρkЕΘF → πtЕyG → οjЕΙH → ξsЕzI → νiЕΚJ → μrЕΑK → λhЕΛL → κqЕΒM → ιgЕΜN → θpЕΓO → ηfЕΝP → ζoЕΔQ → εeЕΞR → δnЕΕS → γdЕΟT → βmЕΖU → αcЕΠV → ΩlЕΗW → ΨbЕΡX → ΧkЕΘY → ΦaЕΣZ → ΥjЕΙa → ΤZЕΤb → ΥgЕΜa → ΤcЕΠb → ΣfЕΝc → ΡbЕΡd → ΣcЕΠc → ΡeЕΞd → ΠbЕΡe → ΣbЕΡc → ΣeЕΞc → ΡcЕΠd
6659 max steps4000wπ → πw3БwG → ψΨЕЕV8 → χΩOζV9 → ξΖrΑnI → ΥI8φνa → ξΤiΚaI → ΥiQδΛa → ΒjRγΚs → zQ8φεu → ξΓ4АqI → φΥBσZA → μθjΙNK → ΠΙOζke → ΖbNηΣo → ΘgGξΝm → ΧWKκΨY → ΞqmΖΓg → XJBσμΨ → θΡoΔcO → ΘeEπΟm → βaKκΤU → ΞvhΛxg → XT1ГβΨ → ВwoΔw4 → ψEЕЕπ8 → χρ7χE9 → πξβSHG → ΩΦwvYW → rm0ДΗΓ → ДKAτλ2 → ВκΞeL4 → ψΝYΥg8 → πlVΨΘG → ΩrLιΒW → Μr9υΒi → μT9υβK → μΠvwdK → Πc0ДΡe → ДeaΣΟ2 → ВhZΤΜ4 → ψjTαΚ8 → πvPεxG → ΩΔ1ГpW → ВrDρΒ4 → ψδ9υR8 → πμzsJG → ΩΡ6ψcW → ςrdΟΒE → δb9υΣS → μzfΝtK → ΠX5ωΧe → τoaΣΕC → θhFοΜO → ΩΘTαlW → vrLιΒy → ΜA2Вυi → АλSβK6 → τΟwveC → θa0ДΤO → ДΘhΛl2 → ВTLιβ4 → ψΜvwh8 → πU0ДαG → ДΩtyV2 → Вs4АΑ4 → ψφ7χ98 → ρομIGF → βΨΡbWU → vqeΞΓy → ZC2ВσΦ → АηkΘO6 → τΗMθmC → θΚJλjO → ΠΘPεle → ΔbLιΣq → ΜgCςΝi → ζWSβΨQ → ΔxpΓvq → EC1Гσς → ВηγRO4 → ψΗytm8 → πK4АλG → φΩΞeVA → μsYΥΑK → Πl7χΘe → πbLιΣG → ΩΜfΝhW → rXTαΧΓ → voAτΕy → κG2ВοM → АΨΛhW6 → τqSβΓC → θxBσvO → θΘ1ГlO → ВΘLιl4 → ψΜLιh8 → πΜTαhG → ΩvTαxW → vr1ГΒy → ВA2Вυ4 → АψκK76 → τρΝfEC → θγWΧSO → ΘyoΔum → LF3Бπλ → ψαΝfU8 → πuWΧyG → Ωp3БΔW → ψrDρΒ8 → πδ9υRG → μΩzsVK → Πs6ψΑe → ςb7χΣE → πδfΝRG → ΩΑWΧsW → rp7χΔΓ → πEAτρG → κγΨVSM → ΜyqΒui → TB3Бτγ → ψιwvM8 → πΛ0ДiG → ДΩRγV2 → ВzrΑt4 → ψ95ωφ8 → τπμIFC → θαΡbUO → ΘueΞym → ZL3БκΦ → ψΝkΘg8 → πWMθΨG → ΩΚpΓjW → rQCςεΓ → ζΓAτqQ → κΔBσpM → θΜDρhO → δΘTαlS → zvLιxu → Μ51ГАi → ВυSβA4 → ψλwvK8 → πΟ0ДeG → ДΩZΤV2 → ВsiΚΑ4 → ψR7χδ8 → ροzsGF → βΨ6ψWU → ςvpΓxE → δD1ГςS → ВεytQ4 → ψΓ4Аq8 → φπBσFA → μθΩUNK → ΠΙszke → bO6ψηΤ → ςΗgΜmE → δVJλΩS → ΠzrΑte → b95ωφΤ → τνgΜIC → θΤUΩaO → ΘthΛzm → TL5ωκγ → τΝwvgC → θW0ДΨO → ДΘpΓl2 → ВMCςι4 → ψζΚiP8 → πΕQδoG → ΩΒFοrW → Ωr9υΒW → μr9υΒK → μΠ9υdK → μΠbΡdK → ΠfbΡΞe → fbXΦΣΟ → ngYΥΝΗ → lWIμΨΙ → ΣqMθΓc → ΚfBσΞk → θYOζΦO → ΘΖlΗnm → MKHνλκ → ΥΟΛhea → jaSβΤΛ → xiQδΛw → ΒS0Дγs → Дy8φu2 → Вξ3БH4 → ωχΥY87 → ςοkΘGE → δΨMθWS → ΚzpΓtk → PD5ωςη → τεΕnQC → θΓGξqO → ΧΘBσlY → θnLιΖO → ΜΘHνli → ΥTLιβa → ΜwiΚwi → TQЕЕδγ → εβ0ДTR → ДΒvwr2 → ВA0Дυ4 → ДψκK72 → ВρΝfE4 → ψγWΧS8 → πyoΔuG → ΩF3БπW → ψαqΒU8 → πuAτyG → κΩ3БVM → ψΜrΑh8 → πU8φαG → ξΩtyVI → Υs4АΑa → φj7χΚA → πμPεJG → ΩΡΓpcW → reCςΟΓ → ζaAτΤQ → κΔhΛpM → ΜTDρβi → δwSβwS → zwЕЕvu → yx2Вvv → А31ГВ6 → ВωσB64 → ψσηNC8 → πηΗlOG → ΩΗKκmW → ΞrJλΒg → ΠX9υΧe → μoaΣΕK → ΠhFοΜe → ΩbTαΣW → vrfΝΒy → XA2ВυΨ → АλoΔK6 → τΟEπeC → θβZΤTO → ΘwiΚwm → RKЕЕκε → λδ4АRL → φΞzsfA → μY6ψΦK → ςΠlΗdE → δcKκΡS → ΞzdΟtg → bX5ωΧΤ → τogΜΕC → θVFοΩO → ΩΘrΑlW → rM8φιΓ → ξΛAτiI → κΥRγZM → ΜzjΙti → TP5ωζγ → τΕwvoC → θG0ДοO → ДΨΗlW2 → ВqKκΓ4 → ψΞBσf8 → πθXΦNG → ΩΙmΖkW → rOIμηΓ → ΣΗAτmc → κfJλΞM → ΠΜXΦhe → nbTαΣΗ → vgIμΝy → ΣW2ВΨc → АqeΞΓ6 → τZBσΥC → ιηjΙON → ΚΗOζmk → ΖPJλζo → ΠΕGξoe → ΧbFοΣY → ΩnfΝΖW → rXHνΧΓ → ΥoAτΕa → κjFοΚM → ΩΜPεhW → ΔrTαΒq → vD9υςy → με2ВQK → АΠΒqd6 → τcAτΡC → κθdΟNM → ΜΙaΣki → hTNηβΝ → ΘwUΩwm → tKЕЕκΑ → λzWΧtL → Ξp5ωΔg → τXDρΧC → θδnΕRO → ΘΑGξsm → ΧL7χκY → πΝmΖgG → ΩWIμΨW → ΣrpΓΒc → fD9υςΟ → μεYΥQK → ΠΓkΘqe → bNBσθΤ → θΙgΜkO → ΘVNηΩm → ΘsKκΑm → ΞL7χκg → πΝWΧgG → ΩpVΨΔW → sqDρΓΒ → δC8φσS → ξηytOI → ΥΗ4Аma → φjJλΚA → μΠPεdK → ΠΔbΡpe → fbDρΣΟ → δgYΥΝS → zlVΨΘu → rM4АιΓ → φΛAτiA → μκRγLK → ΠΝytge → bW4АΨΤ → φqgΜΓA → μVBσΩK → θΠrΑdO → Θc8φΡm → ξeKκΟI → ΥΞZΤfa → kiXΦΛΚ → nSOζγΗ → ΖyIμuo → ΣH3Бξc → ψΦeΞY8 → πmYΥΗG → ΩlJλΘW → ΠrLιΒe → Μb9υΣi → μgSβΝK → ΠxVΨve → rb1ГΣΓ → ВgAτΝ4 → ψκVΨL8 → πΝqΒgG → ΩWAτΨW → κrpΓΒM → ΜD9υςi → μεSβQK → ΠΓwvqe → bC0ДσΤ → ДηgΜO2 → ВΗUΩm4 → ψtJλz8 → πΠ5ωdG → τΩbΡVC → θseΞΑO → ΘZ7χΥm → πkKκΙG → ΩΞNηfW → ΘrXΦΒm → nL9υκΗ → μΝIμgK → ΣΠVΨdc → rfbΡΞΓ → fYAτΦΟ → κmYΥΗM → ΜlJλΘi → ΠTLιβe → ΜwaΣwi → hSЕЕβΝ → γΜCςhT → ζxTαvQ → Δv1Гxq → ВD1Гς4 → ВψδQ74 → ψρΑrE8 → πγ8φSG → ξΩxuVI → Υs2ВΑa → Аj7χΚ6 → τπPεFC → θαΓpUO → ΘuCςym → ζL3БκQ → ψΝΓpg8 → πWCςΨG → ζΩpΓVQ → ΔsCςΑq → ζD7χςQ → πεΓpQG → ΩΓCςqW → ζrBσΒQ → θΔ9υpO → μΘDρlK → δΠLιdS → ΜzbΡti → fT5ωβΟ → τwYΥwC → θkЕЕΘO → ηΙNηkP → ΘΖNηnm → ΘLHνκm → ΥΝKκga → ΞjVΨΚg → rXPεΧΓ → ΔoAτΕq → κGCςοM → ζΨΛhWQ → ΔqSβΓq → xDBσςw → θε0ДQO → ДΘΒql2 → ВMAτι4 → ψκΚiL8 → πΝQδgG → ΩΒVΨrW → sq9υΓΒ → μC8φσK → ξηΟdOI → ΥΗaΣma → jhJλΜΛ → ΠUQδαe → ΒuaΣys → h93БφΝ → ψνUΩI8 → πΤszaG → Ωi6ψΛW → ςrRγΒE → δz9υtS → μz5ωtK → τΠ5ωdC → τθbΡNC → θΙeΞkO → ΘZNηΥm → ΘkKκΙm → ΞOKκηg → ΞΗWΧmg → pXJλΧΕ → ΠoEπΕe → βbFοΣU → ΩvfΝxW → rX1ГΧΓ → ВoAτΕ4 → ψκFοL8 → πΩΜgVG → ΩsUΩΑW → tr7χΒΑ → πA6ψυG → ςλΨVKE → δΟqΒeS → zaAτΤu → κi4АΛM → φΜRγhA → μzTαtK → Πv5ωxe → τb1ГΣC → ВθfΝN4 → ψΙWΧk8 → πpNηΔG → ΩΘDρlW → δrLιΒS → Μz9υti → μT5ωβK → τΠvwdC → θc0ДΡO → ДΘdΟl2 → ВbLιΣ4 → ψΜfΝh8 → πXTαΧG → ΩvnΕxW → rH1ГξΓ → ВΦAτY4 → ψκlΗL8 → πΝKκgG → ΩΞVΨfW → sqXΦΓΒ → nC8φσΗ → ξηIμOI → ΥΣΖmba → jgIμΝΛ → ΣWQδΨc → ΒqeΞΓs → ZC8φσΦ → ξηkΘOI → ΥΗMθma → ΚjJλΚk → ΠQOζεe → ΖΓaΣqo → hHBσξΝ → θΦUΩYO → ΘtlΗzm → MK5ωλκ → τΟΛheC → θaSβΤO → ΘxhΛvm → TL1Гκγ → ВΝwvg4 → ψW0ДΨ8 → ДπpΓF2 → ВαCςU4 → ψζtyP8 → πΕ4АoG → φΩFοVA → μΩrΑVK → Πs8φΑe → ξb7χΣI → πΥfΝZG → ΩkWΧΙW → rpNηΔΓ → ΘEAτρm → κγKκSM → ΞΜxuhg → XU2ВαΨ → АuoΔy6 → τF3БπC → ψθΩUN8 → πΙszkG → ΩO6ψηW → ςΗqΒmE → δKAτλS → κΟyteM → Μa4АΤi → φiSβΛA → μxRγvK → Πz1Гte → Вb5ωΣ4 → ψτfΝB8 → πιWΧMG → ΩΛoΔiW → rSEπγΓ → βyAτuU → κv3БxM → ψΜ1Гh8 → ВπTαF4 → ψαuxU8 → πu2ВyG → АΩ3БV6 → ψτrΑB8 → πι8φMG → ξΩΚiVI → ΥsQδΑa → Βj7χΚs → πQ8φεG → ξΩΒqVI → ΥsAτΑa → κj7χΚM → πΜPεhG → ΩΔTαpW → vrDρΒy → δA2ВυS → АλytK6 → τΟ4АeC → φθZΤNA → μΙiΚkK → ΠRNηδe → ΘΑaΣsm → hL7χκΝ → πΝUΩgG → ΩtVΨzW → sq5ωΓΒ → τC8φσC → ξθζONI → ΥΙΕnka → jOGξηΛ → ΧΗQδmY → ΒnJλΖs → ΠI8φνe → ξΤaΣaI → ΥigΜΛa → jVRγΩΛ → zsQδΑu → Β84Аχs → φο8φGA → ξμΧWJI → ΥΡoΔca → jeEπΟΛ → βaQδΤU → ΒvhΛxs → T91Гφγ → ВνwvI4 → ψΤ0Дa8 → ДπhΛF2 → ВαSβU4 → ψxtyv8 → π51ГАG → ВυΨVA4 → ψλqΒK8 → πΟAτeG → κΩZΤVM → ΜsiΚΑi → TR7χδγ → πΑwvsG → Ω80ДχW → ДοqΒG2 → ВΨAτW4 → ψκpΓL8 → πΝCςgG → ζΩVΨVQ → ΔsqΒΑq → DB7χτσ → πιεPMG → ΩΛΓpiW → rSCςγΓ → ζyAτuQ → κΔ3БpM → ψΜDρh8 → πδTαRG → ΩΑuxsW → r82ВχΓ → АοAτG6 → τκΧWLC → θΝoΔgO → ΘWEπΨm → βqKκΓU → ΞvBσxg → θX1ГΧO → ВΘnΕl4 → ψMGξι8 → πΧΚiXG → ΩoQδΕW → ΒrFοΒs → ΩA8φυW → ξλqΒKI → ΥΟAτea → κjZΤΚM → ΜjPεΚi → ΔTPεβq → ΔwCςwq → ζCЕЕςQ → σεBσQD → θζΒqPO → ΘΕAτom → κLFοκM → ΩΝΛhgW → rWSβΨΓ → xqAτΓw → κC0ДσM → ДηΛhO2 → ВΗSβm4 → ψxJλv8 → πΠ1ГdG → ВΩbΡV4 → ψseΞΑ8 → πZ7χΥG → πΩjΙVG → ΩsOζΑW → Ζr7χΒo → πH9υξG → μΩΥYVK → ΠskΘΑe → bN7χθΤ → πΙgΜkG → ΩVNηΩW