Base 144: 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 steps100
216 max steps20 → 1Я → Э3Щ7СFБVΤΒωXΟΖПHχZΛΚЯ1Э3
374 max steps100 → 0аа → Яа1 → Юа2 → Эа3 → Ьа4 → Ыа5 → Ъа6 → Ща7 → Ша8 → Ча9 → ЦаA → ХаB → ФаC → УаD → ТаE → СаF → РаG → ПаH → ОаI → НаJ → МаK → ЛаL → КаM → ЙаN → ИаO → ЗаP → ЖаQ → ЕаR → ДаS → ГаT → ВаU → БаV → АаW → ωаX → ψаY → χаZ → φаa → υаb → τаc → σаd → ςаe → ρаf → πаg → οаh → ξаi → νаj → μаk → λаl → κаm → ιаn → θаo → ηаp → ζаq → εаr → δаs → γаt → βаu → αаv → Ωаw → Ψаx → Χаy → Φаz → ΥаΑ → ΤаΒ → ΣаΓ → ΡаΔ → ΠаΕ → ΟаΖ → ΞаΗ → ΝаΘ → ΜаΙ → ΛаΚ → ΚаΛΚаΛ
424 max steps2007 → 71ЮЪ → ЭТD4 → ЩДR8 → СβtG → БVАW → ΥΡΓΒ → IDТП → ЕφZS → γΚΚu → VааБ → БUБW → ΦΣΒΑ → KFРН → БςdW → ΤΒΣΓ → HEСР → ГψXU → ΨΞΖy → O7ШЙ → СκlG → БlκWΤlκΓmFРλБlκW
558 max steps10003 → 30аЯЮ → аЫа41 → ЯЫа42 → ЮЪа53 → ЭШа74 → ЬХаA5 → ЫСаE6 → ЪМаJ7 → ЩЖаP8 → ШωаW9 → ЧρаeA → ЦθаnB → ХΧаxC → ФΛаΙD → УyаΦE → ТΘаΜF → СxаΧG → РΗаΝH → ПwаΨI → ОΖаΞJ → НvаΩK → МΕаΟL → ЛuаαM → КΔаΠN → ЙtаβO → ИΓаΡP → ЗsаγQ → ЖΒаΣR → ЕrаδS → ДΑаΤT → ГqаεU → ВzаΥV → БpаζW → АyаΦX → ωoаηY → ψxаΧZ → χnаθa → φwаΨb → υmаιc → τvаΩd → σlаκe → ςuаαf → ρkаλg → πtаβh → οjаμi → ξsаγj → νiаνk → ξpаζj → νlаκk → μoаηl → λkаλm → μlаκl → λnаθm → κkаλn → μkаλl → μnаθl → λlаκmλlаκm