Base 180: 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

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
292 max steps20 → 1イ → ア3э7хFеVЕΒΝτЗzΕВαθчDйRНtΗАιΩуHбZχΚυΜГΔΦμзTЙxΑЖΙψρΠУnΤξЯbσΞЛvΓДΡπЧjγζ2ィя5щBнNХlΨκпLЩhηβ4ァы9сJЭdοΣЫfλΧлPСpΟςПrΛφωΘνΥгXБΖεδ0ゥイ1ア3
392 max steps100 → 0ゥゥ → イゥ1 → ィゥ2 → アゥ3 → ァゥ4 → яゥ5 → юゥ6 → эゥ7 → ьゥ8 → ыゥ9 → ъゥA → щゥB → шゥC → чゥD → цゥE → хゥF → фゥG → уゥH → тゥI → сゥJ → рゥK → пゥL → оゥM → нゥN → мゥO → лゥP → кゥQ → йゥR → иゥS → зゥT → жゥU → еゥV → дゥW → гゥX → вゥY → бゥZ → аゥa → Яゥb → Юゥc → Эゥd → Ьゥe → Ыゥf → Ъゥg → Щゥh → Шゥi → Чゥj → Цゥk → Хゥl → Фゥm → Уゥn → Тゥo → Сゥp → Рゥq → Пゥr → Оゥs → Нゥt → Мゥu → Лゥv → Кゥw → Йゥx → Иゥy → Зゥz → ЖゥΑ → ЕゥΒ → ДゥΓ → ГゥΔ → ВゥΕ → БゥΖ → АゥΗ → ωゥΘ → ψゥΙ → χゥΚ → φゥΛ → υゥΜ → τゥΝ → σゥΞ → ςゥΟ → ρゥΠ → πゥΡ → οゥΣ → ξゥΤ → νゥΥ → μゥΦ → λゥΧ → κゥΨ → ιゥΩ → θゥα → ηゥβ → ζゥγ → εゥδ → δゥεδゥε
422 max stepsB00j → jAщШ → пδδM → Шゥゥi → ШhШj → ηδδγ → 3ゥゥア → ア2ア4 → яь76 → щфFC → ндVOХДΒmΨpРλΟBшσнRиOХМtmΨΖАλiBшЩнζβOХ3ァmэΧκ8хBшGндVO
571 max steps1000A → A0ゥイы → ゥшゥB1 → イшゥB2 → ィчゥC3 → アхゥE4 → ァтゥH5 → яоゥL6 → юйゥQ7 → эгゥW8 → ьЬゥd9 → ыФゥlA → ъЛゥuB → щБゥΕC → шπゥΠD → чδゥδE → цΟゥρF → хγゥεG → фΞゥςH → уβゥζI → тΝゥσJ → сαゥηK → рΜゥτL → пΩゥθM → оΛゥυN → нΨゥιO → мΚゥφP → лΧゥκQ → кΙゥχR → йΦゥλS → иΘゥψT → зΥゥμU → жΗゥωV → еΤゥνW → дΖゥАX → гΣゥξY → вΕゥБZ → бΡゥοa → аΔゥВb → ЯΠゥπc → ЮΓゥГd → ЭΟゥρe → ЬΒゥДf → ЫΞゥςg → ЪΑゥЕh → ЩΝゥσi → ШzゥЖj → ЧΜゥτk → ЦyゥЗl → ХΛゥυm → ФxゥИn → УΚゥφo → ТwゥЙp → СΙゥχq → РvゥКr → ПΘゥψs → ОuゥЛt → НΗゥωu → МtゥМv → НΔゥВu → МwゥЙv → ЛΓゥГw → КvゥКx → ЛzゥЖw → КyゥЗx → ЙyゥЗy → ИxゥИz → ЙvゥКy → ЛyゥЗw → КzゥЖx → ЙxゥИyЙxゥИy