Base 142: 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 steps1 → 0 → 0
262 max steps20 → 1Э → Ы3 → Ч7 → ПF → ωV → ΡΒ → EР → БT → Φx → MИ → λj → oζ → eπ → yΥ → KК → οf → wΧ → OЖ → ηn → gξ → uΩ → SВ → Ψv → QД → γr → Yφ → ΛΘ → 2Ь → Щ5 → УB → ЗN → ιl → kκ → mθ → iμ → qδ → aτ → ΗΜ → 4Ъ → Х9 → ЛJ → ρd → ΑΣ → GО → χX → ΝΖ → 6Ш → СD → ГR → αt → UА → Τz → IМ → σb → ΕΞ → 8Ц → НH → υZ → ΙΚ → 0Ю → Э1 → Ы3
373 max steps100 → 0ЮЮ → ЭЮ1 → ЬЮ2 → ЫЮ3 → ЪЮ4 → ЩЮ5 → ШЮ6 → ЧЮ7 → ЦЮ8 → ХЮ9 → ФЮA → УЮB → ТЮC → СЮD → РЮE → ПЮF → ОЮG → НЮH → МЮI → ЛЮJ → КЮK → ЙЮL → ИЮM → ЗЮN → ЖЮO → ЕЮP → ДЮQ → ГЮR → ВЮS → БЮT → АЮU → ωЮV → ψЮW → χЮX → φЮY → υЮZ → τЮa → σЮb → ςЮc → ρЮd → πЮe → οЮf → ξЮg → νЮh → μЮi → λЮj → κЮk → ιЮl → θЮm → ηЮn → ζЮo → εЮp → δЮq → γЮr → βЮs → αЮt → ΩЮu → ΨЮv → ΧЮw → ΦЮx → ΥЮy → ΤЮz → ΣЮΑ → ΡЮΒ → ΠЮΓ → ΟЮΔ → ΞЮΕ → ΝЮΖ → ΜЮΗ → ΛЮΘ → ΚЮΙ → ΙЮΚ → ΙЮΚ
442 max stepsI00r → rHМδ → υZτa → ΚΗΛΚ → 3ЮЮЫ → Ы2Ы4 → ЩЦ76 → УОFC → ЗψVO → ιΠΒm → kDРλ → ГnζS → αfξu → wTАΨ → ΦPДy → εLИq → νbςi → ΕrβΟ → Y9Фχ → ЛΜΖK → ρ5Шe → УzΣC → ЗHМO → υθla → ΙjκΛ → o1Ьη → Ыfξ4 → ЧvΧ8 → ПPДG → ωδpW → ΡbςΓ → ΕDРΟ → Г9ФS → ЛΩtK → ρTАe → ΦzΣy → MHМЙ → υμha → ΙrβΛ → Y1Ьχ → ЫΜΖ4 → Ч5Ш8 → УОFC
559 max steps10000 → 0ЮЮЮЮ → ЭЮЮЮ1 → Э0ЮЭ2 → ЮЪЮ31 → ЭЪЮ32 → ЬЩЮ43 → ЫЧЮ64 → ЪФЮ95 → ЩРЮD6 → ШЛЮI7 → ЧЕЮO8 → ЦψЮV9 → ХπЮdA → ФηЮmB → УΦЮwC → ТΚЮΘD → СxЮΥE → РΗЮΛF → ПwЮΦG → ОΖЮΜH → НvЮΧI → МΕЮΝJ → ЛuЮΨK → КΔЮΞL → ЙtЮΩM → ИΓЮΟN → ЗsЮαO → ЖΒЮΠP → ЕrЮβQ → ДΑЮΡR → ГqЮγS → ВzЮΣT → БpЮδU → АyЮΤV → ωoЮεW → ψxЮΥX → χnЮζY → φwЮΦZ → υmЮηa → τvЮΧb → σlЮθc → ςuЮΨd → ρkЮιe → πtЮΩf → οjЮκg → ξsЮαh → νiЮλi → μrЮβj → λhЮμk → νoЮεi → μlЮθj → λnЮζk → κkЮιl → κlЮθl → ιlЮθm → ιjЮκm → λkЮιk → κnЮζl → ιjЮκm