Base 140: 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

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
248 max steps20 → 1Ы → Щ3Х7НFχVΟΒГPγpΕΜПDБRΨtΦvεnιjΡzυXΛΖУ9ЙJοdρbΓΞЗLλhΙΘЫ1Щ3
372 max steps100 → 0ЬЬ → ЫЬ1 → ЪЬ2 → ЩЬ3 → ШЬ4 → ЧЬ5 → ЦЬ6 → ХЬ7 → ФЬ8 → УЬ9 → ТЬA → СЬB → РЬC → ПЬD → ОЬE → НЬF → МЬG → ЛЬH → КЬI → ЙЬJ → ИЬK → ЗЬL → ЖЬM → ЕЬN → ДЬO → ГЬP → ВЬQ → БЬR → АЬS → ωЬT → ψЬU → χЬV → φЬW → υЬX → τЬY → σЬZ → ςЬa → ρЬb → πЬc → οЬd → ξЬe → νЬf → μЬg → λЬh → κЬi → ιЬj → θЬk → ηЬl → ζЬm → εЬn → δЬo → γЬp → βЬq → αЬr → ΩЬs → ΨЬt → ΧЬu → ΦЬv → ΥЬw → ΤЬx → ΣЬy → ΡЬz → ΠЬΑ → ΟЬΒ → ΞЬΓ → ΝЬΔ → ΜЬΕ → ΛЬΖ → ΚЬΗ → ΙЬΘ → ΘЬΙΘЬΙ
422 max stepsD00M → MCПЗ → ГκhQ → γpβq → bYσς → ΙΔΜΙ → 7ЬЬХ → Х6Х8 → ПМFE → БφVS → ΨΞΒuSBРБЕΧtOηRАmΨhκuqRАγΨZςuΗRАΛΨ3ШuХRА8НΧtGχRАWΨΞΒu
557 max steps10000 → 0ЬЬЬЬ → ЫЬЬЬ1 → Ы0ЬЫ2 → ЬШЬ31 → ЫШЬ32 → ЪЧЬ43 → ЩХЬ64 → ШТЬ95 → ЧОЬD6 → ЦЙЬI7 → ХГЬO8 → ФφЬV9 → УξЬdA → ТεЬmB → СΤЬwC → РΘЬΘD → ПvЬΥE → ОΗЬΙF → НuЬΦG → МΖЬΚH → ЛtЬΧI → КΕЬΛJ → ЙsЬΨK → ИΔЬΜL → ЗrЬΩM → ЖΓЬΝN → ЕqЬαO → ДΒЬΞP → ГpЬβQ → ВΑЬΟR → БoЬγS → АzЬΠT → ωnЬδU → ψyЬΡV → χmЬεW → φxЬΣX → υlЬζY → τwЬΤZ → σkЬηa → ςvЬΥb → ρjЬθc → πuЬΦd → οiЬιe → ξtЬΧf → νhЬκg → μsЬΨh → λgЬλi → μpЬβh → λjЬθi → κoЬγj → ιiЬιk → κlЬζj → ιlЬζkθkЬηlθjЬθlιjЬθkιlЬζk