Base 150: 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
217 max steps20 → 1е → г3Я7ЧFЗVαΒσjΨΔБbΝΞе1г3
377 max steps100 → 0жж → еж1 → дж2 → гж3 → вж4 → бж5 → аж6 → Яж7 → Юж8 → Эж9 → ЬжA → ЫжB → ЪжC → ЩжD → ШжE → ЧжF → ЦжG → ХжH → ФжI → УжJ → ТжK → СжL → РжM → ПжN → ОжO → НжP → МжQ → ЛжR → КжS → ЙжT → ИжU → ЗжV → ЖжW → ЕжX → ДжY → ГжZ → Вжa → Бжb → Ажc → ωжd → ψжe → χжf → φжg → υжh → τжi → σжj → ςжk → ρжl → πжm → οжn → ξжo → νжp → μжq → λжr → κжs → ιжt → θжu → ηжv → ζжw → εжx → δжy → γжz → βжΑ → αжΒ → ΩжΓ → ΨжΔ → ΧжΕ → ΦжΖ → ΥжΗ → ΤжΘ → ΣжΙ → ΡжΚ → ΠжΛ → ΟжΜ → ΞжΝ → ΝжΞΝжΞ
427 max stepsJ00u → uIУι → БbАc → ΞΛΟΞ → 3жжг → г2г4 → бЮ76 → ЫЦFCПЖVOρΩΒmsLРλυfφiΕzβΨQHФНГμpaΡjςΛw5аηЫXДCПΥΖOρDШmЛrκSιfφuΕbАΨΝHФΟГ1дaгΠΚ4Я5а8ЫЦFC
560 max steps10006 → 60жеб → жЮж71 → еЮж72 → дЭж83 → гЫжA4 → вШжD5 → бФжH6 → аПжM7 → ЯЙжS8 → ЮВжZ9 → ЭτжhA → ЬλжqB → ЫαжΑC → ЪΞжΜD → ЩΒжΩE → ШΛжΟF → ЧΑжαG → ЦΚжΠH → ХzжβI → ФΙжΡJ → УyжγK → ТΘжΣL → СxжδM → РΗжΤN → ПwжεO → ОΖжΥP → НvжζQ → МΕжΦR → ЛuжηS → КΔжΧT → ЙtжθU → ИΓжΨV → ЗsжιW → ЖΒжΩX → ЕrжκY → ДΑжαZ → Гqжλa → Вzжβb → Бpжμc → Аyжγd → ωoжνe → ψxжδf → χnжξg → φwжεh → υmжοi → τvжζj → σlжπk → ςuжηl → ρkжρm → ςrжκl → ρnжξm → πqжλn → οmжοo → πnжξn → οpжμo → ξmжοp → πmжοn → πpжμn → οnжξoοnжξo