Base 131: 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 steps1 → 0 → 0
29 max steps10 → 0У → Т1 → Р3 → М7 → ДF → ξV → ΖΒ → 3Р → М7
368 max steps100 → 0УУ → ТУ1 → СУ2 → РУ3 → ПУ4 → ОУ5 → НУ6 → МУ7 → ЛУ8 → КУ9 → ЙУA → ИУB → ЗУC → ЖУD → ЕУE → ДУF → ГУG → ВУH → БУI → АУJ → ωУK → ψУL → χУM → φУN → υУO → τУP → σУQ → ςУR → ρУS → πУT → οУU → ξУV → νУW → μУX → λУY → κУZ → ιУa → θУb → ηУc → ζУd → εУe → δУf → γУg → βУh → αУi → ΩУj → ΨУk → ΧУl → ΦУm → ΥУn → ΤУo → ΣУp → ΡУq → ΠУr → ΟУs → ΞУt → ΝУu → ΜУv → ΛУw → ΚУx → ΙУy → ΘУz → ΗУΑ → ΖУΒ → ΕУΓ → ΔУΔ → ΓУΕ → ΔУΔ
469 max stepsΕ000 → ΔУУΔ → ΔΓΔΕ → 1УУТ → Т0Т2 → ТП32 → РЛ74 → МГF8 → ДνVG → ξΕΒW → Ζ2РΓ → О2Р6 → ОЗB6 → ИυNC → φΦlO → ΧYκm → zYκΙ → z8КΙ → В8КI → ВιZI → κwΚa → xCЖΛ → τCЖQ → τΡpQ → ΣQςq → ΠQςs → ΠMφs → ΩMφk → Ωcζk → rcζΡ → rOτΡ → ΥOτo → ΥUξo → ΘUξΑ → Θ6МΑ → Ж6МE → ЖρRE → ςΝtS → ΞIАu → θIАc → θsΞc → tKψΟ → δKψg → δkΧg → laθΨ → vaθΝ → vGВΝ → μGВY → μΑΖY → Β4ОΗ → К4ОA → КωJA → АεdK → ζoΣe → pSπΤ → ΜSπw → ΜEДw → πEДU → πΙxU → ΚAИy → ψAИM → ψαhM → βgβi → jgβα → jeδα → neδΦ → nWμΦ → ΔWμΕ → Δ0ТΕ → Т0Т2
553 max steps30000 → 2УУУС → С1УС3 → ТНУ52 → СМУ63 → РКУ84 → ПЗУB5 → ОГУF6 → НψУK7 → МςУQ8 → ЛλУX9 → КγУfA → ЙΣУoB → ИΘУyC → ЗwУΚD → ЖxУΙE → ЕvУΛF → ДwУΚG → ГuУΜH → ВvУΛI → БtУΝJ → АuУΜK → ωsУΞL → ψtУΝM → χrУΟN → φsУΞO → υqУΠP → τrУΟQ → σpУΡR → ςqУΠS → ρoУΣT → πpУΡU → οnУΤV → ξoУΣW → νmУΥX → μnУΤY → λlУΦZ → κmУΥa → ιkУΧb → θlУΦc → ηjУΨd → ζkУΧe → εiУΩf → δjУΨg → γhУαh → βiУΩi → αgУβj → γfУγh → δiУΩg → γiУΩh → βhУαi → βgУβi → γgУβh → γiУΩh
6262 max stepsi000μμ → μμhαXY → ΓΒgβΖΖ → j42РПα → ОЛeδ86 → ИГmΥGC → φνWμWO → ΧΕΓΔΓm → Z20ТСλ → ТПyΘ42 → РЛ8К84 → МГБHG8 → ДνιZWG → ξΕwΚΓW → ΖD1СЖΓ → Рσ2РQ4 → ОМΠq76 → ИЕOτEC → φρΤnSO → ΧΝUξum → ΘZHБκΑ → κy6МΙa → Жx9ЙΚE → АςBЗRK → φζΞsdO → ΧqKψΡm → δZPσκg → ΣykΧΙq → bR9Йςι → АΟuΜsK → ζMGВχe → μαoΣiY → ΒgSπγΗ → Μk4ОΨw → КcEДηA → АπrΟTK → ζΛMφwe → ΩpDЕΣk → ςdRρζS → ΟΝpΡut → RLHБψσ → κγΟrga → xkMφΨΛ → ΩcCЖηk → τscζΟQ → ΣrLχΠq → βRNυςi → ΧΟgβsm → jZLχκα → βyeδΙi → nh9ЙβΦ → АiWμαK → ζΔfγΔe → pkУУΧΤ → ΨΣ2Рpl → ОbRρθ6 → ИΞtΝtC → φKIАωO → θεΦlec → toYκΤΟ → zUKψοΙ → δΙ8Кyg → Вl9ЙΧI → АκZιZK → ζywΚΙe → pD9ЙЖΤ → АσSπQK → ζΡΛvqe → pQEДσΤ → πΡSπqU → ΜΚPσxw → ΣFBЗДq → φοQςUO → ΧΠΘyrm → ZO8Кυλ → ВΦyΘmI → κY8Кλa → ВΑwΚΗI → κD5НЖa → ИσwΚQC → φΡCЖqO → τΧPσlQ → ΤΡZιqp → xTPσπΛ → ΣΛCЖwq → τRDЕςQ → ςΣΞspS → ΞSKψρu → δΝIАug → θlHБΧc → κtZιΞa → ywJωΛΚ → ζEAИЕe → ψρoΣSM → βΝSπui → ΜhHБβw → κiEДαa → πxfγΚU → ΚlBЗΧy → φaAИιO → ψΧvΛlM → βaEДιi → πwgβΛU → ΚjDЕΩy → ςeAИεS → ψΞnΤtM → βVJωξi → ζΗgβΑe → pj5НΩΤ → ИeSπεC → φΜnΤvO → ΧVFГξm → ξΗYκΑW → Ζz5НΘΓ → И82РЛC → ОГυNG6 → ИνΦlWC → φΕYκΓO → Χz1СΘm → РZ7Лκ4 → МДxΙF8 → ДοAИUG → ψξΘyVM → βΗ8КΑi → Вh5НβI → ИκhαZC → φygβΙO → Χj9ЙΩm → АeYκεK → ζznΤΘe → pV7ЛξΤ → ДΗSπΑG → ξΜ5НvW → ИΖFГΒC → φξ3ПVO → МΧΖΑl8 → Дa4ОιG → КξvΛVA → АΗEДΑK → πζ5НdU → ИΚpΡxC → φRBЗςO → φΧΞslO → ΧaKψιm → δwYκΛg → zlDЕΧΙ → ςa8КιS → ВΞvΛtI → κKEДωa → πεwΚeU → ΚoCЖΤy → τUAИοQ → ψΣΘypM → βS8Кρi → ВΝgβuI → κjHБΩa → κxdεΚa → xpBЗΣΛ → φSCЖρO → τΧΜulQ → ΣaGВιq → μwQςΛY → ΠΒDЕΖs → ςN3ПφS → МΨΝtk8 → ДcIАηG → ξθrΟbW → ΖuMφΝΓ → ΩI2РБk → Оιcζa6 → ИwqΠΛC → φPDЕτO → ςΧΣolS → ΞaSπιu → ΜwIАΛw → θFDЕДc → ςοsΞUS → ΞΙKψyu → δJ9ЙАg → АηkΧcK → ζsaθΟe → vpLχΣΝ → βSGВρi → μΝgβuY → ΒjHБΩΗ → κe4Оεa → КxnΤΚA → АVBЗξK → φζΖΑdO → Χq4ОΡm → КZPσκA → АΣxΙpK → ζSAИρe → ψΝoΣuM → βTHБπi → κΛgβwa → xjDЕΩΛ → ςeCЖεS → τΞnΤtQ → ΣVJωξq → ζΗQςΑe → Πp5НΣs → ИSMφρC → φΩΜujO → ΧeGВεm → μoYκΤY → ΒzTοΘΗ → Κ84ОЛy → КГAИGA → АψμWLK → ζγΓΔge → pk0ТΨΤ → ТcSπη2 → РΜrΟv4 → МNFГφ8 → ДξΧkVG → ξΗaθΑW → Ζv5НΜΓ → ИG2РГC → ОφμWN6 → ИΨΓΔkC → φc0ТηO → ТΧrΟl2 → РaMφι4 → МΩvΛj8 → ДeEДεG → πξnΤVU → ΚΗUξΑy → ΘB5НИΑ → Иχ6МMC → ЖφΩiNE → ςΨeδkS → ΞnbηΥu → tWIАνΟ → θΕKψΓc → δt1СΞg → РlJωΧ4 → МζZιd8 → ДxpΡΚG → ξRBЗςW → φΟΕΒsO → ΧM2Рχm → ОαYκi6 → ИzfγΘC → φl7ЛΧO → ДΧZιlG → ξxZιΚW → ΖxBЗΚΓ → φC2РЗO → ОυΦlO6 → ИΦYκmC → φzXλΘO → ΧΒ7ЛΖm → ДZ3ПκG → МξxΙV8 → ДΗAИΑG → ψξ5НVM → ИβΖΑhC → φi4ОαO → КΧfγlA → АlZιΧK → ζxZιΚe → xpBЗΣΛ