Base 154: 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 steps1 → 0 → 0
222 max steps20 → 1й → з3 → г7 → ЫF → ЛV → εΒ → QР → οr → kφ → yθ → WК → γΔ → MФ → χj → Αζ → SО → λv → cД → ΟΠ → 0к → й1 → з3
379 max steps100 → 0кк → йк1 → ик2 → зк3 → жк4 → ек5 → дк6 → гк7 → вк8 → бк9 → акA → ЯкB → ЮкC → ЭкD → ЬкE → ЫкF → ЪкG → ЩкH → ШкI → ЧкJ → ЦкK → ХкL → ФкM → УкN → ТкO → СкP → РкQ → ПкR → ОкS → НкT → МкU → ЛкV → КкW → ЙкX → ИкY → ЗкZ → Жкa → Екb → Дкc → Гкd → Вкe → Бкf → Акg → ωкh → ψкi → χкj → φкk → υкl → τкm → σкn → ςкo → ρкp → πкq → οкr → ξкs → νкt → μкu → λкv → κкw → ιкx → θкy → ηкz → ζкΑ → εкΒ → δкΓ → γкΔ → βкΕ → αкΖ → ΩкΗ → ΨкΘ → ΧкΙ → ΦкΚ → ΥкΛ → ΤкΜ → ΣкΝ → ΡкΞ → ΠкΟ → ΟкΠ → ΟкΠ
437 max stepsJ00w → wIЧλ → ЕbДc → ΣΟΟΞ → 3ккз → з2з4 → ев76 → ЯЪFC → УКVO → υδΒm → wPРλ → ρbДq → ΡnςΟ → s1иο → зjφ4 → гzζ8 → ЫTМG → ЛθxW → εXИΓ → αPРΗ → ρHШq → Зnςa → ΦrξΛ → k9аχ → ЧzζK → ГTМe → ιΜΣy → Y5дЙ → ЯΩΖC → УHШO → Зτla → ΦvκΛ → c9аЕ → ЧΠΞK → Г1иe → зΜΣ4 → г5д8 → ЯЪFC
561 max steps10008 → 80кйг → как91 → йак92 → иЯкA3 → зЭкC4 → жЪкF5 → еЦкJ6 → дСкO7 → гЛкU8 → вДкb9 → бφкjA → аνкsB → ЯγкΓC → ЮΠкΞD → ЭΔкβE → ЬΝкΡF → ЫΓкγG → ЪΜкΣH → ЩΒкδI → ШΛкΤJ → ЧΑкεK → ЦΚкΥL → ХzкζM → ФΙкΦN → УyкηO → ТΘкΧP → СxкθQ → РΗкΨR → ПwкιS → ОΖкΩT → НvкκU → МΕкαV → ЛuкλW → КΔкβX → ЙtкμY → ИΓкγZ → Зsкνa → ЖΒкδb → Еrкξc → ДΑкεd → Гqкοe → Вzкζf → Бpкπg → Аyкηh → ωoкρi → ψxкθj → χnкςk → φwкιl → υmкσm → τvкκn → σlкτo → υsкνm → τpкπn → σrкξo → ςoкρp → ςpкπp → ρpкπq → ρnкςq → σoкρo → ςrкξp → ρnкςq