Base 135: Maximum Iteration Sequences: Cycle Start

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
Cycle Start
11 max steps10
25 max steps10 → 0Ч → Ц1 → Ф3 → Р7 → ИF
368 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
44 max stepsΗ000 → ΖЧЧΖ → ΖΕΖΗ → 1ЧЧЦ → Ц0Ц2
555 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
6193 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