Base 145: 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
212 max steps10 → 0б → а1 → Ю3Ъ7ТFВVΥΒψZΜΚЮ3
375 max steps100 → 0бб → аб1 → Яб2 → Юб3 → Эб4 → Ьб5 → Ыб6 → Ъб7 → Щб8 → Шб9 → ЧбA → ЦбB → ХбC → ФбD → УбE → ТбF → СбG → РбH → ПбI → ОбJ → НбK → МбL → ЛбM → КбN → ЙбO → ИбP → ЗбQ → ЖбR → ЕбS → ДбT → ГбU → ВбV → БбW → АбX → ωбY → ψбZ → χбa → φбb → υбc → τбd → σбe → ςбf → ρбg → πбh → οбi → ξбj → νбk → μбl → λбm → κбn → ιбo → θбp → ηбq → ζбr → εбs → δбt → γбu → βбv → αбw → Ωбx → Ψбy → Χбz → ΦбΑ → ΥбΒ → ΤбΓ → ΣбΔ → ΡбΕ → ΠбΖ → ΟбΗ → ΞбΘ → ΝбΙ → ΜбΚ → ΛбΛΚбΜΛбΛ
418 max stepsΜ000 → ΛббΛ → ΛΚΛΜ → 1бба → а0а2аЭ32ЮЩ74ЪСF8ТБVGВΤΒWΥGРΓАGРYАΟΖYΠ8ШΗР8ШIРχZIψΛΚaΜ0аΛа0а2
559 max steps10000 → 0бббб → аббб1 → а0ба2 → бЭб31 → аЭб32 → ЯЬб43 → ЮЪб64 → ЭЧб95 → ЬУбD6 → ЫОбI7 → ЪИбO8 → ЩБбV9 → ШσбdA → ЧκбmB → ЦΩбwC → ХΝбΘD → ФΑбΥE → УΗбΞF → ТzбΦG → СΖбΟH → РyбΧI → ПΕбΠJ → ОxбΨK → НΔбΡL → МwбΩM → ЛΓбΣN → КvбαO → ЙΒбΤP → ИuбβQ → ЗΑбΥR → ЖtбγS → ЕzбΦT → ДsбδU → ГyбΧV → ВrбεW → БxбΨX → АqбζY → ωwбΩZ → ψpбηa → χvбαb → φoбθc → υuбβd → τnбιe → σtбγf → ςmбκg → ρsбδh → πlбλi → οrбεj → ξkбμk → νqбζl → μjбνm → ξnбιk → νnбιl → μmбκm → λmбκn → λkбμnνlбλlμoбθmλkбμn