Base 165: 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
244 max steps10 → 0х → ф1 → т3 → о7 → жF → ЦV → πΒ → bР → δΞ → Dи → ЪR → ψt → rА → vφ → nД → Δξ → XФ → μΖ → TШ → τx → jИ → Μζ → Hд → ТZ → θΚ → Lа → Кh → Πβ → 9м → вJ → Оd → ΩΣ → 5р → кB → ЮN → Жl → Θκ → PЬ → Вp → zς → fМ → ΥΧ → 1ф → т3
385 max steps100 → 0хх → фх1 → ух2 → тх3 → сх4 → рх5 → пх6 → ох7 → нх8 → мх9 → лхA → кхB → йхC → ихD → зхE → жхF → ехG → дхH → гхI → вхJ → бхK → ахL → ЯхM → ЮхN → ЭхO → ЬхP → ЫхQ → ЪхR → ЩхS → ШхT → ЧхU → ЦхV → ХхW → ФхX → УхY → ТхZ → Схa → Рхb → Пхc → Охd → Нхe → Мхf → Лхg → Кхh → Йхi → Ихj → Зхk → Жхl → Ехm → Дхn → Гхo → Вхp → Бхq → Ахr → ωхs → ψхt → χхu → φхv → υхw → τхx → σхy → ςхz → ρхΑ → πхΒ → οхΓ → ξхΔ → νхΕ → μхΖ → λхΗ → κхΘ → ιхΙ → θхΚ → ηхΛ → ζхΜ → εхΝ → δхΞ → γхΟ → βхΠ → αхΡ → ΩхΣ → ΨхΤ → ΧхΥ → ΦхΦ → ΥхΧ → ΦхΦ
424 max stepsΧ000 → ΦххΦ → ΦΥΦΧ → 1ххф → ф0ф2 → фс32 → тн74 → оеF8 → жХVG → ЦοΒW → πaРΓ → ζaРΝ → ζGдΝ → ФGдY → ФλΖY → μSШΗ → φSШw → φmДw → ΖmДν → ΖUЦν → ςUЦΑ → ςeМΑ → ΧeМΦ → Χ0фΦ → ф0ф2
565 max steps30000 → 2ххху → у1ху3 → фпх52 → уох63 → тмх84 → сйхB5 → рехF6 → пахK7 → оЪхQ8 → нУхX9 → мЛхfA → лВхoB → кςхyC → йηхΚD → иΤхΧE → зΙхθF → жΣхΨG → еΘхιH → дΡхΩI → гΗхκJ → вΠхαK → бΖхλL → аΟхβM → ЯΕхμN → ЮΞхγO → ЭΔхνP → ЬΝхδQ → ЫΓхξR → ЪΜхεS → ЩΒхοT → ШΛхζU → ЧΑхπV → ЦΚхηW → ХzхρX → ФΙхθY → УyхςZ → ТΘхιa → Сxхσb → РΗхκc → Пwхτd → ОΖхλe → Нvхυf → МΕхμg → Лuхφh → КΔхνi → Йtхχj → ИΓхξk → Зsхψl → ЖΒхοm → Еrхωn → ДΑхπo → ГqхАp → Вzхρq → БpхБr → Вwхτq → Бsхψr → Аvхυs → ωrхωt → Аsхψs → ωuхφt → ψrхωu → Аrхωs → Аuхφs → ωsхψt → ωsхψt