Base 155: 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
216 max steps10 → 0л → к1 → и3 → д7ЬFМVζΒξtΖβДdΞΣд7
380 max steps100 → 0лл → кл1 → йл2 → ил3 → зл4 → жл5 → ел6 → дл7 → гл8 → вл9 → блA → алB → ЯлC → ЮлD → ЭлE → ЬлF → ЫлG → ЪлH → ЩлI → ШлJ → ЧлK → ЦлL → ХлM → ФлN → УлO → ТлP → СлQ → РлR → ПлS → ОлT → НлU → МлV → ЛлW → КлX → ЙлY → ИлZ → Злa → Жлb → Елc → Длd → Глe → Влf → Блg → Алh → ωлi → ψлj → χлk → φлl → υлm → τлn → σлo → ςлp → ρлq → πлr → οлs → ξлt → νлu → μлv → λлw → κлx → ιлy → θлz → ηлΑ → ζлΒ → εлΓ → δлΔ → γлΕ → βлΖ → αлΗ → ΩлΘ → ΨлΙ → ΧлΚ → ΦлΛ → ΥлΜ → ΤлΝ → ΣлΞ → ΡлΟ → ΠлΠΟлΡΠлΠ
424 max stepsΡ000 → ΠллΠ → ΠΟΠΡ → 1ллк → к0к2кз32иг74дЫF8ЬЛVGМεΒWζQРΓπQРsπkφszkφιzWКιδWКΕδMФΕψMФkψΑζkΒSОημSОwμcДwΠcДΡΠ0кΡк0к2
561 max stepsΟ0000 → ΞлллΣ → ΣΝлΣΟ → Τ2лиΞ → йΞлΡ3 → иΟлΠ4 → зΝлΣ5 → жΞлΡ6 → еΜлΤ7 → дΝлΣ8 → гΛлΥ9 → вΜлΤA → бΚлΦB → аΛлΥC → ЯΙлΧD → ЮΚлΦE → ЭΘлΨF → ЬΙлΧG → ЫΗлΩH → ЪΘлΨI → ЩΖлαJ → ШΗлΩK → ЧΕлβL → ЦΖлαM → ХΔлγN → ФΕлβO → УΓлδP → ТΔлγQ → СΒлεR → РΓлδS → ПΑлζT → ОΒлεU → НzлηV → МΑлζW → ЛyлθX → КzлηY → ЙxлιZ → Иyлθa → Зwлκb → Жxлιc → Еvлλd → Дwлκe → Гuлμf → Вvлλg → Бtлνh → Аuлμi → ωsлξj → ψtлνk → χrлοl → φsлξm → υqлπn → τrлοo → σpлρp → ςqлπq → ρoлςr → σnлσp → τqлπo → σqлπpςpлρqςoлςqσoлςpσqлπp