Base 153: 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
233 max steps10 → 0й → и1 → ж3в7ЪFКVδΒπpθxΩΖЖZΥΚЦJВdΜΣЮBТNτlΠΞж3
379 max steps100 → 0йй → ий1 → зй2 → жй3 → ей4 → дй5 → гй6 → вй7 → бй8 → ай9 → ЯйA → ЮйB → ЭйC → ЬйD → ЫйE → ЪйF → ЩйG → ШйH → ЧйI → ЦйJ → ХйK → ФйL → УйM → ТйN → СйO → РйP → ПйQ → ОйR → НйS → МйT → ЛйU → КйV → ЙйW → ИйX → ЗйY → ЖйZ → Ейa → Дйb → Гйc → Вйd → Бйe → Айf → ωйg → ψйh → χйi → φйj → υйk → τйl → σйm → ςйn → ρйo → πйp → οйq → ξйr → νйs → μйt → λйu → κйv → ιйw → θйx → ηйy → ζйz → εйΑ → δйΒ → γйΓ → βйΔ → αйΕ → ΩйΖ → ΨйΗ → ΧйΘ → ΦйΙ → ΥйΚ → ΤйΛ → ΣйΜ → ΡйΝ → ΠйΞ → ΟйΟΞйΠΟйΟ
428 max stepsΠ000 → ΟййΟ → ΟΞΟΠ → 1ййи → и0и2ие32жб74вЩF8ЪЙVGКγΒWδOРΓςOРoςqξorkτοxkτιxYЖιΧYЖΙΧCЬΙРCЬQРοpQπmςqtmςνtgψνΖgψαΖIЦαДIЦcДΟΞcΠ0иΟи0и2
561 max steps1000J → J0йиЧ → йФйK1 → иФйK2 → зУйL3 → жСйN4 → еОйQ5 → дКйU6 → гЕйZ7 → вωйf8 → бςйm9 → аκйuA → ЯαйΔB → ЮΟйΞC → ЭΔйαD → ЬΝйΠE → ЫΓйβF → ЪΜйΡG → ЩΒйγH → ШΛйΣI → ЧΑйδJ → ЦΚйΤK → ХzйεL → ФΙйΥM → УyйζN → ТΘйΦO → СxйηP → РΗйΧQ → ПwйθR → ОΖйΨS → НvйιT → МΕйΩU → ЛuйκV → КΔйαW → ЙtйλX → ИΓйβY → ЗsйμZ → ЖΒйγa → Еrйνb → ДΑйδc → Гqйξd → Вzйεe → Бpйοf → Аyйζg → ωoйπh → ψxйηi → χnйρj → φwйθk → υmйςl → τvйιm → σlйσn → τsйμm → σoйπn → ςrйνo → ρnйρp → ςoйπo → ρqйξp → πnйρq → ςnйρo → ςqйξo → ρoйπpρoйπp