Base 159: 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
29 max steps10 → 0п → о1 → м3 → и7 → аF → РV → κΒκΒ
382 max steps100 → 0пп → оп1 → нп2 → мп3 → лп4 → кп5 → йп6 → ип7 → зп8 → жп9 → епA → дпB → гпC → впD → бпE → апF → ЯпG → ЮпH → ЭпI → ЬпJ → ЫпK → ЪпL → ЩпM → ШпN → ЧпO → ЦпP → ХпQ → ФпR → УпS → ТпT → СпU → РпV → ПпW → ОпX → НпY → МпZ → Лпa → Кпb → Йпc → Ипd → Зпe → Жпf → Епg → Дпh → Гпi → Впj → Бпk → Апl → ωпm → ψпn → χпo → φпp → υпq → τпr → σпs → ςпt → ρпu → πпv → οпw → ξпx → νпy → μпz → λпΑ → κпΒ → ιпΓ → θпΔ → ηпΕ → ζпΖ → εпΗ → δпΘ → γпΙ → βпΚ → αпΛ → ΩпΜ → ΨпΝ → ΧпΞ → ΦпΟ → ΥпΠ → ΤпΡ → ΣпΣΡпΤΣпΣ
456 max stepsΤ000 → ΣппΣ → ΣΡΣΤ → 1ппо → о0о2ол32мз74иЯF8аПVGРιΒWκUРΓμUРΑμYМΑδYМΙδIЬΙКIЬcКΦΞcΧ6иΟв6иEвУREФρtSςkАuΔkАιΔSТιπSТwπgДwΜgДαΜCвαЦCвQЦυpQφsςqtmψσzmψνzaКνΩaКΝΩAдΝЪAдMЪГhMДΙβiΚGЮγОGЮYОεΖYζMШΗВMШkВΕζkΖOЦηψOЦoψwξoxeЖοΠeЖΦΠ4кΦж4кAжЫJAЬЗdKИΡΣeΣ0оΤо0о2
563 max steps1000M → M0поЪ → пЧпN1 → оЧпN2 → нЦпO3 → мФпQ4 → лСпT5 → кНпX6 → йИпc7 → иВпi8 → зυпp9 → жνпxA → еδпΗB → дΣпΡC → гΗпδD → вΠпΤE → бΖпεF → аΟпΥG → ЯΕпζH → ЮΞпΦI → ЭΔпηJ → ЬΝпΧK → ЫΓпθL → ЪΜпΨM → ЩΒпιN → ШΛпΩO → ЧΑпκP → ЦΚпαQ → ХzпλR → ФΙпβS → УyпμT → ТΘпγU → СxпνV → РΗпδW → ПwпξX → ОΖпεY → НvпοZ → МΕпζa → Лuпπb → КΔпηc → Йtпρd → ИΓпθe → Зsпςf → ЖΒпιg → Еrпσh → ДΑпκi → Гqпτj → Вzпλk → Бpпυl → Аyпμm → ωoпφn → ψxпνo → χnпχp → ψuпπo → χqпτp → φtпρq → υpпυr → φqпτq → υsпςr → τpпυs → φpпυq → φsпςq → υqпτrυqпτr