Base 164: 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
стуфхцчшщъыьэюяァ

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
222 max steps20 → 1у → с3 → н7 → еF → ХV → οΒ → aР → εΜ → Gд → УX → λΖ → SШ → υv → mД → Εμ → UЦ → ρz → eМ → ΦΥ → 0ф → у1 → с3
384 max steps100 → 0фф → уф1 → тф2 → сф3 → рф4 → пф5 → оф6 → нф7 → мф8 → лф9 → кфA → йфB → ифC → зфD → жфE → ефF → дфG → гфH → вфI → бфJ → афK → ЯфL → ЮфM → ЭфN → ЬфO → ЫфP → ЪфQ → ЩфR → ШфS → ЧфT → ЦфU → ХфV → ФфW → УфX → ТфY → СфZ → Рфa → Пфb → Офc → Нфd → Мфe → Лфf → Кфg → Йфh → Ифi → Зфj → Жфk → Ефl → Дфm → Гфn → Вфo → Бфp → Афq → ωфr → ψфs → χфt → φфu → υфv → τфw → σфx → ςфy → ρфz → πфΑ → οфΒ → ξфΓ → νфΔ → μфΕ → λфΖ → κфΗ → ιфΘ → θфΙ → ηфΚ → ζфΛ → εфΜ → δфΝ → γфΞ → βфΟ → αфΠ → ΩфΡ → ΨфΣ → ΧфΤ → ΦфΥ → ΥфΦ → ΥфΦ
420 max steps500a → a4пС → лζΚA → бJаK → ОЛed → αΥΥΡ → 7ффн → н6н8 → здFE → ЩФVS → χξΒu → qZРБ → ηxςΛ → iJаЙ → НΞβe → ΨBиΤ → Э3рO → нДl8 → еΖκG → ХRШW → χξΒu
565 max stepsΥ0000 → ΤфффΧ → ΧΣфΧΥ → Ψ1фтΤ → уΤфΦ2 → тΥфΥ3 → сΣфΧ4 → рΤфΦ5 → пΡфΨ6 → оΣфΧ7 → нΠфΩ8 → мΡфΨ9 → лΟфαA → кΠфΩB → йΞфβC → иΟфαD → зΝфγE → жΞфβF → еΜфδG → дΝфγH → гΛфεI → вΜфδJ → бΚфζK → аΛфεL → ЯΙфηM → ЮΚфζN → ЭΘфθO → ЬΙфηP → ЫΗфιQ → ЪΘфθR → ЩΖфκS → ШΗфιT → ЧΕфλU → ЦΖфκV → ХΔфμW → ФΕфλX → УΓфνY → ТΔфμZ → СΒфξa → РΓфνb → ПΑфοc → ОΒфξd → Нzфπe → МΑфοf → Лyфρg → Кzфπh → Йxфςi → Иyфρj → Зwфσk → Жxфςl → Еvфτm → Дwфσn → Гuфυo → Вvфτp → Бtфφq → Аuфυr → ωsфχs → ψtфφt → χrфψu → ωqфωs → Аtфφr → ωtфφs → ψsфχt → ψrфψt → ωrфψs → ωtфφs