Base 113: 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
212 max steps10 → 0Б → А1 → ψ3τ7μFΥVΩRvtψ3
359 max steps100 → 0ББ → АБ1 → ωБ2 → ψБ3 → χБ4 → φБ5 → υБ6 → τБ7 → σБ8 → ςБ9 → ρБA → πБB → οБC → ξБD → νБE → μБF → λБG → κБH → ιБI → θБJ → ηБK → ζБL → εБM → δБN → γБO → βБP → αБQ → ΩБR → ΨБS → ΧБT → ΦБU → ΥБV → ΤБW → ΣБX → ΡБY → ΠБZ → ΟБa → ΞБb → ΝБc → ΜБd → ΛБe → ΚБf → ΙБg → ΘБh → ΗБi → ΖБj → ΕБk → ΔБl → ΓБm → ΒБn → ΑБo → zБp → yБq → xБr → wБs → vБt → uБutБvuБu
418 max stepsv000 → uББu → utuv → 1ББА → А0А2Аχ32ψσ74τλF8μΤVGΥmΒWnEμΓΧEμUΧqxUr6τyξ6τEξΨREΩutSv0АuА0А2
547 max steps30000 → 2БББω → ω1Бω3 → АυБ52 → ωτБ63 → ψςБ84 → χοБB5 → φλБF6 → υζБK7 → τΩБQ8 → σΡБX9 → ςΙБfA → ρzБoB → πpБyC → οnБΑD → ξoБzE → νmБΒF → μnБΑG → λlБΓH → κmБΒI → ιkБΔJ → θlБΓK → ηjБΕL → ζkБΔM → εiБΖN → δjБΕO → γhБΗP → βiБΖQ → αgБΘR → ΩhБΗS → ΨfБΙT → ΧgБΘU → ΦeБΚV → ΥfБΙW → ΤdБΛX → ΣeБΚY → ΡcБΜZ → ΠdБΛa → ΟbБΝb → ΞcБΜc → ΝaБΞd → ΟZБΟb → ΠcБΜa → ΟcБΜbΞbБΝcΞaБΞcΟaБΞbΟcБΜb
6430 max stepsf000ιι → ιιeΚIJ → ΟΞUΥbb → pdbΝΜΑ → bYAπΡΟ → ζicΜΗM → ΘZNγΠi → ΔgOβΙm → ΒSGκΨo → ΣuCξuY → βiББΖQ → αΗJηiR → ΜxNγre → ΔX5υΣm → πkGκΕC → δΣJηXO → ΜΔjΕle → XLHιζΤ → ΠΙkΔga → fSIθΨΛ → ΞuUΥuc → paББΞΑ → ΟzCξpb → βd9ρΜQ → θzXΡpK → Μj9ρΖe → θXLεΣK → ΜΘjΕhe → XQKζαΤ → ΚykΔqg → TJ7σθΨ → μΝsvcG → Υa2ψΟW → φndΛΒ6 → πXDνΣC → δΩjΕRO → ΔwKζsm → ΚH3χκg → τΡSΧY8 → μthΗvG → ΥP1ωβW → ψΑmΒo4 → τFBομ8 → μδΥUNG → ΥΕozkW → nKAπηΓ → ζΛEμeM → ΧΘVΤhU → rnPαΒy → zE6τνq → ξΨ8ςSE → κΩtuRI → Πw0Аsa → Аf3χΚ2 → ψτTΦ74 → τνqxE8 → μΨ6τSG → ξΥtuVE → Ωo0АΑS → АvBοt2 → ψδ1ωN4 → ψτΔk74 → τνIθE8 → μΨΝbSG → ΥuaΞuW → ncББΜΓ → ΝΒ8ςnd → κZDνΠI → ΩΠfΙZS → vgSΧΙu → tS0АΨw → Аu2ψu2 → ψυББ54 → χφ2ψ55 → φςπA96 → πιεLIC → δΟΗhaO → ΔeOβΛm → ΒWGκΤo → ΣmCξΓY → βjFλΖQ → ΥzLεpW → Θn9ρΒi → θPDνβK → ΩΜzodS → vYAπΡu → ζi0АΗM → АΘNγh2 → ψΔPαl4 → τzHιp8 → μΠ9ρZG → θΥfΙVK → ΜoSΧΑe → tXBοΣw → δk2ψΕO → φΔJηl6 → πΜHιdC → δΠXΡZO → ΔjfΙΖm → TMGκεΨ → ΣΗsviY → jO2ψγΗ → φΓMδm6 → πΖFλjC → δΥLεVO → ΘΔnΑli → PICξιγ → βΟΑnaQ → zeCξΛq → βW8ςΤQ → κzlΓpI → ΠH9ρκa → θΡeΚYK → ΜiUΥΗe → pXNγΣΑ → ΔkAπΕm → ζKGκηM → ΣΛΗheY → jWOβΤΗ → ΒmMδΓo → ΖGCξλk → βΤKζWQ → ΚzlΓpg → TH9ρκΨ → θΡsvYK → Μi2ψΗe → φXNγΣ6 → πΔjΕlC → δLHιζO → ΠΙΓlga → fSGκΨΛ → ΣuUΥuY → piББΖΑ → Ηz4φpj → ςN9ρδA → ιηΔkKJ → ΞΛIθec → ΞbVΤΞc → ncaΞΝΓ → daEμΟΝ → ΧeYΠΛU → rhVΤΘy → nQ6ταΓ → ξyEμqE → ΩΧ7σTS → μvrwtG → Υ51ωφW → ψρmΒA4 → τηEμK8 → μΧΚeTG → ΥsUΥwW → pn3χΒΑ → τEAπν8 → μζΧSLG → ΥΙsvgW → nS2ψΨΓ → φuEμu6 → πΦББTC → οΧIθTD → βΞrwbQ → zc4φΝq → ςa8ςΟA → κθdΛJI → ΠΝWΣca → lfZΟΚΕ → fUIθΦΛ → ΞqUΥyc → pb7σΞΑ → μcAπΝG → ζΥZΟVM → ΘoeΚΑi → VPBοβΦ → δΑozoO → ΔCAποm → ζγGκOM → ΣΘΒmhY → jQEμαΗ → ΧyMδqU → Ζr7σxk → μL5υζG → πΥΘgVC → δoQΩΑO → ΔxBοrm → δH5υκO → πΡΓlYC → δiGκΗO → ΣΔNγlY → ΔjHιΖm → ΠMGκεa → ΣΗeΚiY → jVNγΥΗ → ΔoMδΑm → ΖHBοκk → δΡKζYO → ΚΔhΗlg → TPHιβΨ → ΠΑsvoa → fC2ψοΛ → φγUΥO6 → πΓozmC → δGAπλO → ζΤΓlWM → ΘmGκΓi → ΣPFλβY → ΥΑiΖoW → nNBοδΓ → δΕEμkO → ΧΔJηlU → ΜrHιxe → ΠX5υΣa → πkeΚΕC → δVJηΥO → ΜΔnΑle → XICξιΤ → βΟkΔaQ → zeIθΛq → ΞW8ςΤc → κmaΞΓI → ΠdFλΜa → ΥfXΡΚW → njTΦΖΓ → rMEμεy → ΧΗ6τiU → ξrNγxE → ΩΔ5υlS → πvHιtC → δΠ1ωZO → ψΔfΙl4 → τTHιΧ8 → μΠrwZG → Υg4φΙW → ςnRΨΒA → θvDνtKΩΜ1ωdSψvXΡt4τj1ωΖ8ψμLεF4τΦΗhU8μqOβyGΥΒ7σnWμnDνΒGΩΥDνVSΩvnΑtSvD1ωξuψα0АQ4Аτxq72ψν6τE4τξΧSD8μαsvQGΥy2ψqWφn7σΒ6πμDνFCδΩΥUROΔwozsmHB3χπλτεΡXM8μΗiΖiGΥOMδγWΖΓmΒmkLGEμληΧΤΙfWUrmSΧΓytG6τλwξΤ2ψWEφΩlΓR6πwGκsCδΣ3χXOτΔjΕl8μLHιζGΥΠΘgZWngQΩΙΓxSEμΨsΧu4φuUςqББxAρyhΗqBζP7σβMμΘzohGΥQAπαWζymΒqMΘF7σμiμΦOβUGΥΒpynWnE8ςνΓκΨEμSIΧΠtuZUrg0АΙyАS6τΨ2ψξtuD4τα0АQ8АμxqF2ψΦ6τU4τξpyD8μα8ςQGκΥxqVIΠo6τΑaξfBοΚEδΩTΦROΔwqxsmH73χτλτνΡXE8μΨiΖSGΥuMδuWΖmББΒkΕΓ3χmlτJFλθ8μΥΜcVGΥoYΠΑWnhBοΘΓδQEμαOΧΔxqlUrI6τιyξΟ6τaEξΩdΛREΩwWΣsSvl3χΔuτI0Аι8АμΞaF2ψΦcΜU4τqYΠy8μh7σΘGμΥPαVGΥznΑpWnD9ρξΓθαEμQKΧΜxqdUrY6τΡyξi6τΗEξΩNγREΩΔvslSvI2ψιuφΟ0Аa6АπdΛB2ψεWΣM4τΗkΔi8μOIθγGΥΞΒmbWncEμΝΓΧaEμΟUΧrdΛxUrX5υΣyπk6τΕCξδJηNEΩΜΔkdSvYIθΡuΞi0АΗcАbNγΞ2ψΔbΝl4τbHιΞ8μΠbΝZGΥgaΞΙWndRΨΜΓvYEμΡuΧi0АΗUАrNγx2ψΔ5υl4τπHιB8μεΟZMGΥΗeΚiWnVNγΥΓΔoEμΑmΧHBοκUδΡqxYOΔi6τΗmξOGκγEΩΣΒmXSvkEμΕuΧK0АηUАΛqxe2ψW6τΤ4τξlΓD8μαGκQGΥΣxqXWnk6τΕΓξKEμηEΩΧΚeTSvsUΥwup40АχΑАσAπ82ψλεLG4τΤΗhW8μmOβΓGΥΒFλnWΥnDνΒWΩnDνΒSΩvDνtSΩv1ωtSψv1ωt4ψτ1ω74ψτμE74τνΦTE8μΨqxSGΥu6τuWξmББΒEνΓZΟmFΧfFλΚUΥrTΦxWrn5υΒyπE6τνCξδΧSNEΩΕsvkSvK2ψηuφΛ0Аe6АπVΤB2ψεmΒM4τΗEμi8μΧNγTGΥΔrwlWnI4φιΓςΟEμaAθΧdΛTKΜsWΣwelX3χΣΕτkIθΕ8μΞJηbGΥΜbΝdWnbXΡΞΓjcEμΝΗΧaMδΟUΖrdΛxkXL5υζΤπΙkΔgCδSIθΨOΞΔtulcbI0АιΟАΟcΜa2ψeYΠΛ4τhVΤΘ8μnPαΒGΥzDνpWΩn9ρΒSθvDνtK