Base 133: Maximum Iteration Sequences: Cycle Start

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
Cycle Start
11 max steps10
23 max steps10 → 0Х → Ф1 → Т3
367 max steps100 → 0ХХ → ФХ1 → УХ2 → ТХ3 → СХ4 → РХ5 → ПХ6 → ОХ7 → НХ8 → МХ9 → ЛХA → КХB → ЙХC → ИХD → ЗХE → ЖХF → ЕХG → ДХH → ГХI → ВХJ → БХK → АХL → ωХM → ψХN → χХO → φХP → υХQ → τХR → σХS → ςХT → ρХU → πХV → οХW → ξХX → νХY → μХZ → λХa → κХb → ιХc → θХd → ηХe → ζХf → εХg → δХh → γХi → βХj → αХk → ΩХl → ΨХm → ΧХn → ΦХo → ΥХp → ΤХq → ΣХr → ΡХs → ΠХt → ΟХu → ΞХv → ΝХw → ΜХx → ΛХy → ΚХz → ΙХΑ → ΘХΒ → ΗХΓ → ΖХΔ → ΕХΕ
44 max stepsΖ000 → ΕХХΕ → ΕΔΕΖ → 1ХХФ → Ф0Ф2
551 max steps10009 → 90ХФН → ХКХA1 → ФКХA2 → УЙХB3 → ТЗХD4 → СДХG5 → РАХK6 → ПυХP7 → ОοХV8 → НθХc9 → МΩХkA → ЛΟХtB → КΕХΔC → ЙtХΟD → ИΓХΖE → ЗsХΠF → ЖΒХΗG → ЕrХΡH → ДΑХΘI → ГqХΣJ → ВzХΙK → БpХΤL → АyХΚM → ωoХΥN → ψxХΛO → χnХΦP → φwХΜQ → υmХΧR → τvХΝS → σlХΨT → ςuХΞU → ρkХΩV → πtХΟW → οjХαX → ξsХΠY → νiХβZ → μrХΡa → λhХγb → κqХΣc → ιgХδd → θpХΤe → ηfХεf → ζoХΥg → εeХζh → ηlХΨf → ζiХβg → εkХΩh → δhХγi → δiХβi → γiХβj → γgХδj
6392 max steps10003S → S30ФТτ → ФПΟt62 → ТЙKАC4 → ОχεfO8 → ЖΨmΧmG → πaYμλW → ΘΒxΛΘΓ → D64РПЙ → МЙυPCA → ВχΤpOK → θΨSςme → ΞrZλΣw → zQGДυΛ → ξΤAКqY → АΔRσΖM → δΠ1Уti → ТjLωβ4 → Оδfεh8 → ЖnjαΧG → πfXνζW → ΘΔnΦΖΓ → X51УРο → ТЛΕΔA4 → ОБ0ФK8 → ФЖζeF2 → ТρoΥU4 → ОΛUπy8 → ЖΚBЙzG → ψπ9ЛVO → ВΩΘΑlK → θc6Оιe → ИuqΣΟE → τRJБτS → θΡΟtse → rOKАχΤ → ζΨQτmg → ΣnZλΧs → zYOφνΛ → ΧΓAКΗo → АX3СξM → ОδΔΕh8 → Жk0ФαG → ФπdηV2 → ТΙqΣΑ4 → ОR7Нτ8 → ЗЕΠsGF → ςοMψWU → βΜΖΓxk → fE2ТЗη → РσoΥS6 → КΟUπuC → ψΚJБzO → θΩ9Лle → ВrbιΣK → θvPυΞe → ΥrHГΣq → μTPυςa → ΥΝyΚwq → TGAКЕσ → АοΝvWM → δΗGДΓi → ξj3СβY → ОΔfεΖ8 → Жn1УΧG → ТπXνV4 → ОΙΓΖΑ8 → Ж82ТНG → РЕοVG6 → КοΗΒWC → ψΗ4РΓO → МΩ3СlA → ОВbιJ8 → ЖιuΞcG → πuIВΟW → κΘJБΒc → θv5ПΞe → КrHГΣC → ψμPυZO → ΩΥzΙpm → bU8Мρλ → ДΛwΜyI → μFBЙЖa → ψρyΚUO → ΩΛAКym → АbBЙκM → ψδvΝhO → ΩkGДαm → ξeaκηY → ΔxpΤΜΗ → TE2ТЗσ → РσΝvS6 → КΟGДuC → ψξJБXO → θΩΔΕle → rc0ФιΤ → ФuQτΟ2 → ТΣJБr4 → ОθPυd8 → ЖΥrΡpG → πUOφρW → ΧΛΗΒyo → XC4РЙο → МχΕΔOA → ВΨ0ФmK → ФθZλd2 → ТzrΡΚ4 → ОP9Лφ8 → ЖВΥoJG → πιUπcW → ΚΘtΟΒΑ → L95ПМБ → КГεfIC → ψλmΧaO → ΩyYμΛm → ΒbBЙκΙ → ψw6ОΝO → ИΩFЕlE → τπbιVS → ΠΙuΞΑu → LJ7НВБ → ЖιεfcG → πumΧΟW → ΘZJБμΓ → θΑ4РΙe → Мr7НΣA → ЖВPυJG → πιΤpcW → ΘuSςΟΓ → ΞK4РБw → МηGДeA → ВξpΤXK → θΕSςΕe → ΞqХХΣw → ΤΝ3Сwr → ОRFЕτ8 → ЖπΠsVG → πΙMψΑW → βΘ7НΒk → Жf5ПζG → КπnΦVC → ψΙWξΑO → ΩΖ7НΔm → Жb1УκG → ТπvΝV4 → ОΙGДΑ8 → Жξ7НXG → ЖπΔΕVG → πΙ0ФΑW → ФΘ7НΒ2 → ТЖ5ПF4 → ОКπUB8 → ЖωΙzMG → πγ8МiW → ДΘhγΒI → μj5Пβa → КzfεΚC → ψn9ЛΧO → ВΩXνlK → θΔbιΖe → vr1УΣΟ → ТQIВυ4 → ОκΣqb8 → ЖwQτΝG → πΣFЕrW → πΘPυΒW → ΥΘ5ПΒq → КT5ПςC → КψΜwNC → ψαEЖkO → ςΩdηlU → ΜrbιΣy → vQCИυΟ → φΤIВqQ → κΥRσpc → ΠvTρΞu → ΜLHГАy → μεCИga → φzlΨΚQ → Υb9Лκq → ВwSςΝK → θΞFЕve → πrHГΣW → μΘPυΒa → Υz5ПΚq → КT9ЛςC → ВψΜwNK → θαEЖke → ςrdηΣU → ΜrPυΣy → ΥQCИυq → φΤSςqQ → ΥΞRσvq → ΠTHГςu → μΝKАwa → ζzFЕΚg → πn9ЛΧW → ВΘXνΒK → θΔ5ПΖe → Кr1УΣC → ТψPυN4 → ОαΤpk8 → ЖeSςηG → πΞpΤvW → ΘTHГςΓ → μΝ4Рwa → МzFЕΚA → Вπ9ЛVK → ВθΘΑdK → θs6ОΡe → ИrNχΣE → τΩPυlS → ΥΠbιtq → vTLωςΟ → δΝIВwi → κjFЕβc → πvfεΞW → ΘnHГΧΓ → μY4Рνa → МΓyΚΗA → ВB3СКK → ОωηdM8 → ЖγqΣiG → πiQτγW → ΣΘhγΒs → jP5Пφγ → КΦgδoC → ψlVοΩO → ΩΘbιΒm → vb5ПκΟ → КwIВΝC → ψκFЕbO → πΩvΝlW → ΘcGДιΓ → ξu4РΟY → МΔJБΖA → Вθ1УdK → ТθrΡd4 → ОsOφΡ8 → ЖΧNχnG → πΩXνlW → ΘΔbιΖΓ → v51УРΟ → ТЛIВA4 → ОБιbK8 → ЖηuΞeG → πqIВΤW → κΘRσΒc → Πv5ПΞu → КLHГАC → ψμδgZO → ΩΑkΩΙm → db7Нκι → ЖwsΠΝG → πNFЕψW → παΗΒkW → Θe4РηΓ → Мq4РΤA → МВRσJA → ВιΟtcK → θuKАΟe → ζrJБΣg → θnPυΧe → ΥrXνΣq → ΔTPυςΗ → ΥΝ2Тwq → РTFЕς6 → КπΜwVC → ψΙEЖΑO → ςΩ7НlU → ЖΜbιxG → πvDЗΞW → τΘHГΒS → μΠ5Пta → КzLωΚC → ψδ9ЛhO → ВΩjαlK → θfbιζe → vrnΦΣΟ → XQIВυο → κΤΕΔqc → vS0ФσΟ → ФΟIВu2 → ТκJБb4 → ОθvΝd8 → ЖsGДΡG → πξNχXW → ΩΘΔΕΒm → b60ФПλ → ФЙwΜC2 → ТχEЖO4 → ОςΧmT8 → ЖΝYμwG → πΒFЕΘW → πΘ5ПΒW → КΘ5ПΒC → Кψ5ПNC → КψΩkNC → ψαcθkO → ΩtdηΠm → rbLωκΤ → δwQτΝi → ΣjFЕβs → πgOφεW → ΧΘlΨΒo → bX5Пξλ → КΕwΜΕC → ψEХХЖO → Зχ7НOF → ЖςΧmTG → πΝYμwW → ΘΒFЕΘΓ → π64РПW → МЙΗΒCA → Вχ4РOK → МθΧmdA → ВsYμΡK → θΒNχΘe → Ωr5ПΣm → КbPυκC → ψΥvΝpO → ΩUGДρm → ξΛaκyY → ΔxBЙΜΗ → ψE2ТЗO → РσΨlS6 → КΟaκuC → ψxJБΜO → θΩDЗle → τrbιΣS → ΠvPυΞu → ΥLHГАq → μεSςga → ΞzlΨΚw → bH9ЛДλ → ВνwΜYK → θΓEЖΗe → ςr3СΣU → ОΜPυx8 → ЖΥDЗpG → τπTρVS → ΠΜΘΑxu → LE6ОЗБ → ИσεfSE → τΟmΧuS → ΠZJБμu → θΑKАΙe → ζr7НΣg → ЖnPυΧG → πΥXνpW → ΘΔTρΖΓ → Μ51УРy → ТЛCИA4 → ОБυPK8 → ЖηΤpeG → πqSςΤW → ΞΘRσΒw → ΠH5ПДu → КνKАYC → ψζΒΗfO → Ωo4РΦm → МbVοκA → ВΘvΝΒK → θH5ПДe → КνqΣYC → ψΓQτΗO → ΩΣ3Сrm → ОbPυκ8 → ЖΥvΝpG → πUGДρW → ξΛΗΒyY → ΔC4РЙΗ → Мχ2ТOA → РВΧmJ6 → КιYμcC → ψΒtΟΘO → ΩL5ПАm → КεaκgC → ψxlΨΜO → ΩbDЗκm → τwaκΝS → ΠxFЕΜu → πLDЗАW → τεΗΒgS → Πm4РΨu → МaKАλA → ВζxΛfK → θoCИΦe → φrVοΣQ → ΥΘPυΒq → ΥT5Пςq → КΝSςwC → ψΞFЕvO