Base 148: 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
276 max steps20 → 1г → б3Э7ХFЕVΨΒυfΓΧωbΛΞЯ5ЩBНNοlΑΩρjΡΘУHБZΟΚЫ9СJχdΗΣПLσhιrΕΥЗTγxεvΦΔГXΤΖЛPλpαzνnΙΠЧDЙRηtΝΜг1б3
376 max steps100 → 0дд → гд1 → вд2 → бд3 → ад4 → Яд5 → Юд6 → Эд7 → Ьд8 → Ыд9 → ЪдA → ЩдB → ШдC → ЧдD → ЦдE → ХдF → ФдG → УдH → ТдI → СдJ → РдK → ПдL → ОдM → НдN → МдO → ЛдP → КдQ → ЙдR → ИдS → ЗдT → ЖдU → ЕдV → ДдW → ГдX → ВдY → БдZ → Адa → ωдb → ψдc → χдd → φдe → υдf → τдg → σдh → ςдi → ρдj → πдk → οдl → ξдm → νдn → μдo → λдp → κдq → ιдr → θдs → ηдt → ζдu → εдv → δдw → γдx → βдy → αдz → ΩдΑ → ΨдΒ → ΧдΓ → ΦдΔ → ΥдΕ → ΤдΖ → ΣдΗ → ΡдΘ → ΠдΙ → ΟдΚ → ΞдΛ → ΝдΜ → ΜдΝΜдΝ
428 max steps900b → b8ЫА → УΜΜI → Аддa → АZАb → ΟΜΜΛ → 3ддб → б2б4 → ЯЬ76 → ЩФFC → НДVOοΧΒmqJРλχhςeΗxβΤSBШЙНζtOοZАmΟpκΛi3аσЭxβ8ХRИGЕζtWΨZАΓΟJРΛχ3аeЭΖΣ8ХBШGНДVO
559 max steps10005 → 50дга → дЭд61 → гЭд62 → вЬд73 → бЪд94 → аЧдC5 → ЯУдG6 → ЮОдL7 → ЭИдR8 → ЬБдY9 → ЫσдgA → ЪκдpB → ЩΩдzC → ШΝдΛD → ЧΑдΨE → ЦΚдΞF → ХzдΩG → ФΙдΟH → УyдαI → ТΘдΠJ → СxдβK → РΗдΡL → ПwдγM → ОΖдΣN → НvдδO → МΕдΤP → ЛuдεQ → КΔдΥR → ЙtдζS → ИΓдΦT → ЗsдηU → ЖΒдΧV → ЕrдθW → ДΑдΨX → ГqдιY → ВzдΩZ → Бpдκa → Аyдαb → ωoдλc → ψxдβd → χnдμe → φwдγf → υmдνg → τvдδh → σlдξi → ςuдεj → ρkдοk → πtдζl → οjдπm → ρqдιk → πnдμl → οpдκm → ξmдνn → ξnдμn → νnдμo → νlдξoοmдνmξpдκnνlдξo