Base 135: 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
29 max steps10 → 0Ч → Ц1 → Ф3 → Р7 → ИF → ςV → ΚΒ → 7Р → ИF
370 max steps100 → 0ЧЧ → ЦЧ1 → ХЧ2 → ФЧ3 → УЧ4 → ТЧ5 → СЧ6 → РЧ7 → ПЧ8 → ОЧ9 → НЧA → МЧB → ЛЧC → КЧD → ЙЧE → ИЧF → ЗЧG → ЖЧH → ЕЧI → ДЧJ → ГЧK → ВЧL → БЧM → АЧN → ωЧO → ψЧP → χЧQ → φЧR → υЧS → τЧT → σЧU → ςЧV → ρЧW → πЧX → οЧY → ξЧZ → νЧa → μЧb → λЧc → κЧd → ιЧe → θЧf → ηЧg → ζЧh → εЧi → δЧj → γЧk → βЧl → αЧm → ΩЧn → ΨЧo → ΧЧp → ΦЧq → ΥЧr → ΤЧs → ΣЧt → ΡЧu → ΠЧv → ΟЧw → ΞЧx → ΝЧy → ΜЧz → ΛЧΑ → ΚЧΒ → ΙЧΓ → ΘЧΔ → ΗЧΕ → ΖЧΖ → ΕЧΗ → ΖЧΖ
440 max stepsΗ000 → ΖЧЧΖ → ΖΕΖΗ → 1ЧЧЦ → Ц0Ц2 → ЦУ32 → ФП74 → РЗF8 → ИρVG → ςΙΒW → Κ6РΓ → К6РE → КυRE → φΡtS → ΣMАu → δMАk → δgζk → ngζα → naμα → zaμΝ → zCКΝ → ψCКQ → ψΦpQ → ΧUςq → ΜUςΑ → ΜAМΑ → ВAМM → ВεhM → ζkβi → leθγ → reθΦ → rSτΦ → ΠSτw → ΠIДw → μIДc → μwΞc → xGЖΟ → πGЖY → πΕΖY → Ζ0ЦΗ → Ц0Ц2
556 max steps10000 → 0ЧЧЧЧ → ЦЧЧЧ1 → Ц0ЧЦ2 → ЧУЧ31 → ЦУЧ32 → ХТЧ43 → ФРЧ64 → УНЧ95 → ТЙЧD6 → СДЧI7 → РψЧO8 → ПρЧV9 → ОιЧdA → НΩЧmB → МΞЧwC → ЛΓЧΘD → КvЧΟE → ЙΒЧΙF → ИuЧΠG → ЗΑЧΚH → ЖtЧΡI → ЕzЧΛJ → ДsЧΣK → ГyЧΜL → ВrЧΤM → БxЧΝN → АqЧΥO → ωwЧΞP → ψpЧΦQ → χvЧΟR → φoЧΧS → υuЧΠT → τnЧΨU → σtЧΡV → ςmЧΩW → ρsЧΣX → πlЧαY → οrЧΤZ → ξkЧβa → νqЧΥb → μjЧγc → λpЧΦd → κiЧδe → ιoЧΧf → θhЧεg → ηnЧΨh → ζgЧζi → ηkЧβh → ζjЧγi → εjЧγj → δiЧδk → εgЧζj → ηjЧγh → ζkЧβi → εiЧδj → εiЧδj
6350 max steps4000MТ → ТM3УБ6 → РМδiB8 → ИБiδMG → ςεiδiW → ΚkiδγΓ → jg6Рηε → КoiδΨE → φjXοδS → ΣΖhεΖu → lMЧЧАγ → БβMАlN → εγdιkj → tjfηδΤ → piOψεΨ → ΩkWπγo → ΘgYξηΕ → Δo2ФΨΙ → ТY4Тο6 → ОМΔΗBA → ДБ2ФMK → Тκδid6 → МuiδΡC → АjLБδO → ζβhεli → mkdιγβ → tgcκηΤ → voOψΨΡ → ΩYKВοo → θΕYξΗg → Δp1ХΧΙ → ФW4Тρ4 → РОΘΓ98 → ИЕ4ТIG → ОςμaVA → ДΛyΜΑK → κD9НКe → ДχsΣQK → κΦOψqe → ΩtTσΣo → ΞZNωξy → βΓEИΙm → τd5СκU → МΞtΡxC → АNFЗАO → ςγαlkW → ΚgcκηΓ → vo6РΨΡ → КYKВοE → φθΔΗfS → Σq2ФΦu → ТUMАσ6 → МδΜyjC → АiCКεO → ψβjγlQ → Χhdιζq → tmUςαΤ → ΜcOψλΑ → ΩwAМΟo → ВZHЕξM → ξζΒΙha → Βm6РαΛ → Кc8ОλE → ЖφvΟRI → ξΤIДsa → μΒPχΚc → Χx7ПΞq → ИVFЗςG → σρΚΑWV → ΜΙ8ОΓΑ → ЖB5СМI → МБνZMC → АεΑΚiO → βk8Оγm → ЖgcκηI → ξvnΨΠa → ΒZJГξΛ → κΓ8ОΙe → Жt5СΣI → МξNωZC → АβΒΙlO → βe6Рιm → КscκΤE → φvPχΠS → ΧΣJГtq → κVNωςe → βΛsΣΑm → dP9Нψλ → ДΨuΠoK → κYKВοe → θΕsΣΗg → pP1ХψΨ → ФΨWπo4 → РΘXοΔ8 → ИΖ3УΖG → РρЧЧV8 → ПςOψV9 → ЖΩΚΑnI → ξa8Оνa → ЖΒzΛΚI → ξB7ПМa → ИБΑΚMG → ςε8ОiW → ЖΚjγΒI → ξh7Пζa → ИΒlαΚG → ςd7ПκW → ИΚtΡΒG → ςN7ПАW → ИγΙΒkG → ςg6РηW → КΚnΨΒE → φZ7ПξS → ИΣΒΙtG → ςO6РωW → КαΙΒmE → φc6РλS → КΣvΟtE → φOIДωS → μαΡtmc → xcMАλΟ → δwGЖΟk → πhHЕζY → ξΖlαΖa → ΒcЧЧκΛ → λΚMАΒd → δv7ПΠk → ИhJГζG → ςκlαdW → ΚucκΡΓ → vM6РБΡ → КεKВiE → φθjγfS → ΣqgζΦu → nUMАσα → δΝaμyk → zhDЙζΝ → φmCКαS → ψΣbλtQ → ΧxNωΞq → βVFЗςm → ςΛcκΑW → Κv9НΠΓ → ДK6РГK → КκθedE → φuqΥΡS → ΣTLБτu → ζΟMАwi → δlHЕβk → ξhdιζa → ΒtlαΣΛ → dO8Оωλ → ЖαuΠmI → ξcKВλa → θΒvΟΚg → pJ7ПДΨ → ИλWπcG → ςΘvΟΔW → ΚJ3УДΓ → Рλ6Рc8 → КИvΟFE → φσIДUS → μΣΜytc → xOCКωΟ → ψαGЖmQ → πΧbλpY → ΖxVρΞΗ → ΚG0ЦЗΓ → Цρ6РW2 → ФКΘΓD4 → Рχ4ТQ8 → ОИΥqFA → ДσSτUK → κΠΜyve → tKCКГΤ → ψιOψeQ → ΩΧrΤpo → ZWQφρο → ΥΙΓΘΓs → R64ТСχ → ОЛΤrCA → ДωQφOK → καΤrme → tcQφλΤ → ΥwOψΟs → ΩRHЕφo → ξΤYξsa → ΔΒPχΚΙ → Χ84ТПq → ОЗUςGA → ДρΛzWK → κΙAМΓe → Вt5СΣM → МζNωhC → АβlαlO → βecκιm → vscκΤΡ → vQKВχΡ → θΦKВqg → θpTσΧg → ΞpVρΧy → ΚWEИρΓ → τΙ6РΓU → КΞ5СxE → МφFЗRC → АςΣsVO → βΛOψΑm → Ωd9Нκo → ДuYξΡK → κΔLБΘe → ζt3УΣi → РlNωβ8 → ИβdιlG → ςtdιΣW → ΚtNωΣΓ → βO6Рωm → КαcκmE → φvbλΠS → ΣxJГΞu → κNFЗАe → ςγsΣkW → ΚgOψηΓ → Ωo6РΨo → КZXοξE → φΖΒΙΖS → Σ6ЧЧРu → СΡlαu7 → КdLБκE → φζtΡhS → ΣmMАαu → δcMАλk → δwgζΟk → nhHЕζα → ξmaμαa → ΒzbλΜΛ → xC8ОЛΟ → ЖωGЖOI → πξΩmZY → ΖΓaμΙΗ → z60ЦСΝ → ЦЛCКC2 → ФωχPO4 → РαΦpm8 → ИcUςλG → ςΜvΟzW → ΚJBЛДΓ → Аλ6РcO → КβvΟlE → φeIДιS → μΣrΤtc → xRNωφΟ → βΤGЖsm → πdPχκY → ΧΖtΡΖq → VMЧЧАσ → Бς6РVN → КδΚΑjE → φi8ОεS → ЖΣjγtI → ξhNωζa → βΒlαΚm → ec7Пλκ → ИwsΣΟG → ςPHЕψW → ξΨΙΒoa → ΒY6РοΛ → КΕ8ОΗE → Жφ1ХRI → ФξΣsZ4 → РΓOψΙ8 → ИΩ5СnG → МςZνVC → АΛΑΚΑO → βA8ОНm → ЖГcκKI → ξιuΠea → ΒsKВΤΛ → θQ8Оχg → ЖΦoΧqI → ξXTσπa → ΞΗΑΚΕy → F91ХОЙ → ФЕσTI4 → РνΝxa8 → ИΑEИΛG → τς9НVU → ДΞΚΑxK → κG8ОЗe → ЖρsΣWI → ξΙOψΓa → ΩΒ5СΚo → МZ7ПξC → ИАΒΙNG → ςγ6РkW → КΚfηΒE → φp7ПΧS → ИΣVρtG → ςΚNωΒW → βΚ7ПΒm → Иd7ПκG → ИςtΡVG → ςΛMАΑW → δΚ9НΒk → Дh7ПζK → ИκlαdG → ςucκΡW → ΚvLБΠΓ → ζK6РГi → КιkβeE → φseθΤS → ΣrPχΥu → ΧSMАυq → δΡUςuk → ΜhLБζΑ → ζmAМαi → ВlbλβM → ζxdιΞi → tlFЗβΤ → ςeOψιW → ΩΚrΤΒo → ZR7Пφο → ИΤΓΘsG → ςQ4ТχW → ОΦΙΒqA → ДU6РσK → КκΜydE → φuCКΡS → ψΣLБtQ → ζΧNωpi → βlVρβm → ΚecκιΓ → vs6РΤΡ → КQKВχE → φθΥqfS → ΣqSτΦu → ΠUMАσw → δΝIДyk → μhDЙζc → φxlαΞS → ΣdFЗκu → ςuMАΡW → δΚLБΒk → ζh7Пζi → ИmkβαG → ςfbλθW → ΚxpΦΞΓ → VG6РЗσ → КρΛzWE → φΙAМΓS → ВΣ5СtM → МζNωhC