Base 171: 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
стуфхцчшщъыьэюяァ

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 steps1 → 0 → 0
211 max steps10 → 0ы → ъ1 → ш3 → ф7 → мF → ЬV → φΒ → hР → Χβ → 3ш → ф7
388 max steps100 → 0ыы → ъы1 → щы2 → шы3 → чы4 → цы5 → хы6 → фы7 → уы8 → ты9 → сыA → рыB → пыC → оыD → ныE → мыF → лыG → кыH → йыI → иыJ → зыK → жыL → еыM → дыN → гыO → выP → быQ → аыR → ЯыS → ЮыT → ЭыU → ЬыV → ЫыW → ЪыX → ЩыY → ШыZ → Чыa → Цыb → Хыc → Фыd → Уыe → Тыf → Сыg → Рыh → Пыi → Оыj → Ныk → Мыl → Лыm → Кыn → Йыo → Иыp → Зыq → Жыr → Еыs → Дыt → Гыu → Выv → Быw → Аыx → ωыy → ψыz → χыΑ → φыΒ → υыΓ → τыΔ → σыΕ → ςыΖ → ρыΗ → πыΘ → οыΙ → ξыΚ → νыΛ → μыΜ → λыΝ → κыΞ → ιыΟ → θыΠ → ηыΡ → ζыΣ → εыΤ → δыΥ → γыΦ → βыΧ → αыΨ → ΩыΩ → Ψыα → ΩыΩ
413 max stepsα000 → ΩыыΩ → ΩΨΩα → 1ыыъ → ъ0ъ2 → ъч32 → шу74 → флF8 → мЫVG → ЬυΒW → φgРΓ → ΩgРα → Ω0ъα → ъ0ъ2
567 max steps30000 → 2ыыыщ → щ1ыщ3 → ъхы52 → щфы63 → шты84 → чпыB5 → цлыF6 → хжыK7 → фаыQ8 → уЩыX9 → тСыfA → сИыoB → рψыyC → пνыΚD → оαыΧE → нΜыλF → мΦыβG → лΛыμH → кΥыγI → йΚыνJ → иΤыδK → зΙыξL → жΣыεM → еΘыοN → дΡыζO → гΗыπP → вΠыηQ → бΖыρR → аΟыθS → ЯΕыςT → ЮΞыιU → ЭΔыσV → ЬΝыκW → ЫΓыτX → ЪΜыλY → ЩΒыυZ → ШΛыμa → ЧΑыφb → ЦΚыνc → Хzыχd → ФΙыξe → Уyыψf → ТΘыοg → Сxыωh → РΗыπi → ПwыАj → ОΖыρk → НvыБl → МΕыςm → ЛuыВn → КΔыσo → ЙtыГp → ИΓыτq → ЗsыДr → ЖΒыυs → ЕrыЕt → Жyыψs → ЕuыВt → Дxыωu → ГtыГv → ДuыВu → ГwыАv → ВtыГw → ДtыГu → ДwыАu → ГuыВv → ГuыВv