Base 167: 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
211 max steps10 → 0ч → ц1 → ф3 → р7 → иF → ШV → ςΒ → dР → βΣ → 7р → иF
386 max steps100 → 0чч → цч1 → хч2 → фч3 → уч4 → тч5 → сч6 → рч7 → пч8 → оч9 → нчA → мчB → лчC → кчD → йчE → ичF → зчG → жчH → ечI → дчJ → гчK → вчL → бчM → ачN → ЯчO → ЮчP → ЭчQ → ЬчR → ЫчS → ЪчT → ЩчU → ШчV → ЧчW → ЦчX → ХчY → ФчZ → Учa → Тчb → Счc → Рчd → Пчe → Очf → Нчg → Мчh → Лчi → Кчj → Йчk → Ичl → Зчm → Жчn → Ечo → Дчp → Гчq → Вчr → Бчs → Ачt → ωчu → ψчv → χчw → φчx → υчy → τчz → σчΑ → ςчΒ → ρчΓ → πчΔ → οчΕ → ξчΖ → νчΗ → μчΘ → λчΙ → κчΚ → ιчΛ → θчΜ → ηчΝ → ζчΞ → εчΟ → δчΠ → γчΡ → βчΣ → αчΤ → ΩчΥ → ΨчΦ → ΧчΧ → ΦчΨ → ΧчΧ
487 max stepsΨ000 → ΧччΧ → ΧΦΧΨ → 1ччц → ц0ц2 → цу32 → фп74 → рзF8 → иЧVG → ШρΒW → ςcРΓ → δcРΡ → δAмΡ → вAмM → вЛhM → МΡβi → Σ8оγ → ж8оI → жУZI → ФιΚa → κMаΛ → КMаk → КΝζk → ΞGжη → ЦGжY → ЦνΖY → ξUШΗ → τUШΑ → τgМΑ → ΥgМα → Υ4тα → о4тA → огJA → дПdK → РαΣe → β6рΤ → к6рE → кЫRE → ЬωtS → АsАu → vsАω → vqВω → zqВυ → ziКυ → ΠiКε → ΠCкε → ЮCкQ → ЮГpQ → ДΑςq → ΒeОσ → ΩeОΦ → Ω2фΦ → т2ф6 → тлB6 → мЯNC → аЗlO → ИΙκm → ΚOЮλ → ЖOЮo → ЖΕξo → ΖWЦο → πWЦΕ → πYФΕ → μYФΙ → μQЬΙ → ВQЬs → Вwφs → xmЖχ → ΘmЖν → ΘSЪν → ψSЪw → ψoДw → ΔoДρ → ΔaТρ → θaТΝ → θIдΝ → ТIдc → ТεΞc → ζEиΟ → ЪEиU → ЪυxU → φkИy → ΜkИι → ΜKвι → ОKвg → ОΦΧg → Χ0цΨ → ц0ц2
565 max stepsΦ0000 → ΥчччΩ → ΩΤчΩΦ → α2чфΥ → хΥчΨ3 → фΦчΧ4 → уΤчΩ5 → тΥчΨ6 → сΣчα7 → рΤчΩ8 → пΡчβ9 → оΣчαA → нΠчγB → мΡчβC → лΟчδD → кΠчγE → йΞчεF → иΟчδG → зΝчζH → жΞчεI → еΜчηJ → дΝчζK → гΛчθL → вΜчηM → бΚчιN → аΛчθO → ЯΙчκP → ЮΚчιQ → ЭΘчλR → ЬΙчκS → ЫΗчμT → ЪΘчλU → ЩΖчνV → ШΗчμW → ЧΕчξX → ЦΖчνY → ХΔчοZ → ФΕчξa → УΓчπb → ТΔчοc → СΒчρd → РΓчπe → ПΑчςf → ОΒчρg → Нzчσh → МΑчςi → Лyчτj → Кzчσk → Йxчυl → Иyчτm → Зwчφn → Жxчυo → Еvчχp → Дwчφq → Гuчψr → Вvчχs → Бtчωt → Аuчψu → ωsчАv → БrчБt → Вuчψs → Бuчψt → Аtчωu → АsчАu → БsчАt → Бuчψt