Base 149: Maximum Iteration Sequences: Full Cycle

Blog: The First Pixel: Kaprekar's Constant 6174

Radix Character Encoding
0123456789ABCDEF
GHIJKLMNOPQRSTUV
WXYZabcdefghijkl
mnopqrstuvwxyzΑΒ
ΓΔΕΖΗΘΙΚΛΜΝΞΟΠΡΣ
ΤΥΦΧΨΩαβγδεζηθικ
λμνξοπρςστυφχψωА
БВГДЕЖЗИЙКЛМНОПР
СТУФХЦЧШЩЪЫЬЭЮЯа
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
223 max steps10 → 0е → д1 → в3Ю7ЦFЖVΩΒτhμpΥΖКRθtΜΞв3
377 max steps100 → 0ее → де1 → ге2 → ве3 → бе4 → ае5 → Яе6 → Юе7 → Эе8 → Ье9 → ЫеA → ЪеB → ЩеC → ШеD → ЧеE → ЦеF → ХеG → ФеH → УеI → ТеJ → СеK → РеL → ПеM → ОеN → НеO → МеP → ЛеQ → КеR → ЙеS → ИеT → ЗеU → ЖеV → ЕеW → ДеX → ГеY → ВеZ → Беa → Аеb → ωеc → ψеd → χеe → φеf → υеg → τеh → σеi → ςеj → ρеk → πеl → οеm → ξеn → νеo → μеp → λеq → κеr → ιеs → θеt → ηеu → ζеv → εеw → δеx → γеy → βеz → αеΑ → ΩеΒ → ΨеΓ → ΧеΔ → ΦеΕ → ΥеΖ → ΤеΗ → ΣеΘ → ΡеΙ → ΠеΚ → ΟеΛ → ΞеΜ → ΝеΝΜеΞΝеΝ
478 max stepsΞ000 → ΝееΝ → ΝΜΝΞ → 1еед → д0д2дб32вЭ74ЮХF8ЦЕVGЖΨΒWΩKРΓφKРgφΓΧgΔIТΨАIТcАΛΞcΜ2вΟа2в6аЩB6ЪНNCОοlOπqκmrgτλΒgταΒMОαςMОkςuζkvYВηΣYВΙΣ8ЬΙФ8ЬIФБZIВΟΚaΠ4аΛЬ4аAЬСJAТχdKψΗΣeΘAЪΤРAЪMРσhMτyβizQКγκQКsκeφsΖeφΦΖEЦΦИEЦUИγxUδSИyζSИwζWДwΧWДΕΧGФΕДGФYДΤΖYΥCШΗМCШQМλpQμiςqxiςεxUЖεβUЖΑβOМΑξOМoξmξopmξνpkπνtkπιtcψιΚcψΡΚ6ЮΡШ6ЮEШЙREКηtSθaАuΞaАΝΞ0дΝд0д2
559 max stepsΜ0000 → ΛеееΟ → ΟΚеΟΜ → Π2евΛ → гΛеΞ3 → вΜеΝ4 → бΚеΟ5 → аΛеΞ6 → ЯΙеΠ7 → ЮΚеΟ8 → ЭΘеΡ9 → ЬΙеΠA → ЫΗеΣB → ЪΘеΡC → ЩΖеΤD → ШΗеΣE → ЧΕеΥF → ЦΖеΤG → ХΔеΦH → ФΕеΥI → УΓеΧJ → ТΔеΦK → СΒеΨL → РΓеΧM → ПΑеΩN → ОΒеΨO → НzеαP → МΑеΩQ → ЛyеβR → КzеαS → ЙxеγT → ИyеβU → ЗwеδV → ЖxеγW → ЕvеεX → ДwеδY → ГuеζZ → Вvеεa → Бtеηb → Аuеζc → ωsеθd → ψtеηe → χrеιf → φsеθg → υqеκh → τrеιi → σpеλj → ςqеκk → ρoеμl → πpеλm → οnеνn → ξoеμo → νmеξp → οlеοn → πoеμm → οoеμnξnеνoξmеξoοmеξnοoеμn