Base 128: Maximum Iteration Sequences: Full Cycle

Blog: The First Pixel: Kaprekar's Constant 6174

Radix Character Encoding
0123456789ABCDEF
GHIJKLMNOPQRSTUV
WXYZabcdefghijkl
mnopqrstuvwxyzΑΒ
ΓΔΕΖΗΘΙΚΛΜΝΞΟΠΡΣ
ΤΥΦΧΨΩαβγδεζηθικ
λμνξοπρςστυφχψωА
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
29 max steps20 → 1П → Н3 → Й7 → БF → λV → ΓΒ → 0Р → П1 → Н3
366 max steps100 → 0РР → ПР1 → ОР2 → НР3 → МР4 → ЛР5 → КР6 → ЙР7 → ИР8 → ЗР9 → ЖРA → ЕРB → ДРC → ГРD → ВРE → БРF → АРG → ωРH → ψРI → χРJ → φРK → υРL → τРM → σРN → ςРO → ρРP → πРQ → οРR → ξРS → νРT → μРU → λРV → κРW → ιРX → θРY → ηРZ → ζРa → εРb → δРc → γРd → βРe → αРf → ΩРg → ΨРh → ΧРi → ΦРj → ΥРk → ΤРl → ΣРm → ΡРn → ΠРo → ΟРp → ΞРq → ΝРr → ΜРs → ΛРt → ΚРu → ΙРv → ΘРw → ΗРx → ΖРy → ΕРz → ΔРΑ → ΓРΒ → ΒРΓ → ΒРΓ
418 max steps1004 → 40ПН → ПИ72 → НАF4 → ЙκV8 → БΒΒG → κРРW → κVκX → ΓzΔΓ → 3РРН → Н2Н4 → ЛИ76 → ЕАFC → σκVO → ΤΒΒm → VРРλ → λUλW → ΕΒΒΑ → 3РРН
553 max stepsΒ0000 → ΑРРРΔ → ΔzРΔΒ → Ε1РОΑ → ПΑРΓ2 → ОΒРΒ3 → НzРΔ4 → МΑРΓ5 → ЛyРΕ6 → КzРΔ7 → ЙxРΖ8 → ИyРΕ9 → ЗwРΗA → ЖxРΖB → ЕvРΘC → ДwРΗD → ГuРΙE → ВvРΘF → БtРΚG → АuРΙH → ωsРΛI → ψtРΚJ → χrРΜK → φsРΛL → υqРΝM → τrРΜN → σpРΞO → ςqРΝP → ρoРΟQ → πpРΞR → οnРΠS → ξoРΟT → νmРΡU → μnРΠV → λlРΣW → κmРΡX → ιkРΤY → θlРΣZ → ηjРΥa → ζkРΤb → εiРΦc → δjРΥd → γhРΧe → βiРΦf → αgРΨg → ΩhРΧh → ΨfРΩi → αeРαg → βhРΧf → αhРΧg → ΩgРΨh → ΩfРΩh → αfРΩg → αhРΧg
686 max stepsF000In → nIEБψΣ → νζTμaU → ΘΖsΛyx → IA6ЙЖω → ГφζZKE → οβtΚeS → ΛlFАΤu → λXFАιW → λΓyΕΒW → Γ60ПКΓ → ПГРРC2 → ОДBДC3 → ЛσρON6 → ЕΥΠnkC → σZRξηO → ΤΛuΙtm → WHDВωλ → οθΒΒYS → ΛwРРΗu → ΚΘ3Мwv → ЙEAЕВ8 → БυνSLG → λΩΘvgW → ΓhBДΨΓ → σeРРαO → ςβHψeP → ηΡkΤna → uYSνθΛ → ΙxFАΗw → λC8ЗДW → ωςΒΒOI → ηΡРРma → ζΣDВmb → οsUλΜS → ΛΕIχzu → εG4ЛАc → ЗκpΞWA → χΒNςΓK → γΤ0Пle → ПmWιΣ2 → НΑUλΔ4 → ЙΕ2Нz8 → ЛБ4ЛF6 → ЗЕλUBA → χτΔzMK → γΧ3Мie → ЙmcγΣ8 → БoUλΠG → λΕQοzW → ΝΓ4ЛΒs → ЗK0ПφA → ПχαeJ2 → НδjΥc4 → ЙpZζΟ8 → БuOρΚG → λΡEБnW → νΓSνΒU → ΙΗ0Пxw → ПC8ЗД2 → НωρOH4 → ЙθΠnY8 → БxRξΗG → λΛ8ЗtW → ωΓGωΒI → ιη0ПZY → ПyuΙΖ2 → НE6ЙВ4 → ЙГνSD8 → БπΘvQG → λΞBДqW → σΓMσΒO → ΦΤ0Пlk → ПaWιζ2 → НΑsΛΔ4 → ЙI2Нψ8 → ЛБεaF6 → ЕμrΜUC → σΖJφyO → γΤ6Йle → ГmWιΣE → οΑUλΔS → ΛΕ2Нzu → ЛG4ЛА6 → ЗЕιWBA → χτzΔMK → γΧ3Мie