Base 98: Maximum Iteration Sequences: Full Cycle

Blog: The First Pixel: Kaprekar's Constant 6174

Radix Character Encoding
0123456789ABCDEF
GHIJKLMNOPQRSTUV
WXYZabcdefghijkl
mnopqrstuvwxyzΑΒ
ΓΔΕΖΗΘΙΚΛΜΝΞΟΠΡΣ
ΤΥΦΧΨΩαβγδεζηθικ
λμνξοπρςστυφχψωА

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
217 max steps20 → 1λ → ι3 → ε7 → ΦF → ΕV → YΒ → SΘ → ev → GΥ → ΓX → UΖ → az → OΜ → mn → 0μ → λ1 → ι3
351 max steps100 → 0μμ → λμ1 → κμ2 → ιμ3 → θμ4 → ημ5 → ζμ6 → εμ7 → δμ8 → γμ9 → βμA → αμB → ΩμC → ΨμD → ΧμE → ΦμF → ΥμG → ΤμH → ΣμI → ΡμJ → ΠμK → ΟμL → ΞμM → ΝμN → ΜμO → ΛμP → ΚμQ → ΙμR → ΘμS → ΗμT → ΖμU → ΕμV → ΔμW → ΓμX → ΒμY → ΑμZ → zμa → yμb → xμc → wμd → vμe → uμf → tμg → sμh → rμi → qμj → pμk → oμl → nμm → mμn → mμn
428 max stepsC00b → bBΩz → ΝNΜO → pmml → 3μμι → ι2ι4 → ηδ76 → αΥFC → ΝΔVO → oXΒm → U1κΗ → ιbx4 → εLΞ8 → ΦrhG → Ε9βW → ΡXΒK → wTΖe → cHΣy → ΑLΞa → sPΚi → k9βq → Ρ5ζK → αvdC → ΝHΣO → Αnla → Q1κΛ → ιjp4 → ε5ζ8 → αΥFC
543 max stepsm0000 → lμμμo → okμom → p1μκl → λlμn2 → κmμm3 → ιkμo4 → θlμn5 → ηjμp6 → ζkμo7 → εiμq8 → δjμp9 → γhμrA → βiμqB → αgμsC → ΩhμrD → ΨfμtE → ΧgμsF → ΦeμuG → ΥfμtH → ΤdμvI → ΣeμuJ → ΡcμwK → ΠdμvL → ΟbμxM → ΞcμwN → ΝaμyO → ΜbμxP → ΛZμzQ → ΚaμyR → ΙYμΑS → ΘZμzT → ΗXμΒU → ΖYμΑV → ΕWμΓW → ΔXμΒX → ΓVμΔY → ΕUμΕW → ΖXμΒV → ΕXμΒW → ΔWμΓX → ΔVμΔX → ΕVμΔW → ΕXμΒW
6502 max steps7000Rc → cR6εΙy → ΨhLΞsE → ΙsAαhS → ΟgAαtM → ΟsCΨhM → ΛsAαhQ → ΟkAαpM → Οs4ηhM → γsAαhA → ΡΟAαLK → ΟwsgdM → sJBΩΡi → Νx9βcO → ΡoKΟlK → wu2ιfe → ηIEΦΣ6 → αΗyaTC → ΝdNΜwO → pnIΡml → y40λθc → λδLΞ82 → ιΥrhG4 → εΔ9βW8 → ΦΡWΓJG → ΕxVΔcW → ZXKΟΓΒ → uVRΘΕg → gZDΧΑu → ΙRDΧΙS → ΙhftsS → gEAαΧu → ΟΘDΧSM → ΙseuhS → gGAαΥu → ΟΔDΧWM → ΙsWΓhS → gWAαΔu → ΟXDΧΓM → ΙsUΕhS → gaAαzu → ΟPDΧΛM → ΙskohS → gB3θαu → εΞDΧM8 → ΦΙqiRG → Εh7δsW → ΦYAαΒG → ΟΕSΗVM → seYΑvi → SH9βΤΙ → ΡΒftYK → wTDΧΗe → ΙdHΣwS → ΑgIΡta → yQCΨΚc → ΛjLΞqQ → sk6εpi → ΨA4ηβE → γΠΘRKA → ΡvfteK → wHDΧΤe → ΙΒHΣYS → ΑgSΗta → eQCΨΚw → ΛjHΣqQ → Αk6εpa → ΨQ4ηΚE → γΙiqRA → Ρh7δsK → ΦwAαdG → ΟΕIΡVM → ysYΑhc → SMAαΞΙ → ΟrftiM → sE8γΧi → ΤΘ9βSI → ΡΑeuZK → wRFΥΙe → ΕhHΣsW → ΑYAαΒa → ΟTPΚΗM → skcwpi → KA4ηβΡ → γΠvdKA → ΡvHΣeK → ΑwGΤda → ΓQIΡΚY → yjTΖqc → cM6εΞy → ΨrLΞiE → Ιs8γhS → ΤgAαtI → ΟΑCΨZM → ΛsQΙhQ → kiAαrq → Ο95ζγM → αΣrhIC → Νz9βaO → ΡoOΛlK → wm2ιne → ηI0λΣ6 → λαyaB2 → ιΞNΜM4 → εrnli8 → Φ91κγG → ιΣΔVI4 → εzXΒa8 → ΦUOΛΖG → ΕmaynW → YO0λΜΓ → λnTΖm2 → ιc0λx4 → λεKΟ72 → ιΧtfE4 → εΘDΧS8 → ΦΙeuRG → ΕhFΥsW → ΕYAαΒW → ΟYSΗΒM → seSΗvi → eH9βΤw → ΡΒHΣYK → ΑwSΗda → eQIΡΚw → yjHΣqc → ΑM6εΞa → ΨrPΚiE → Ιk8γpS → Τg4ηtI → γΑCΨZA → ΡΛQΙPK → wlhroe → IA2ιβΤ → ηΠzZK6 → αvPΚeC → ΝkGΤpO → Γo4ηlY → γU2ιΖA → ηΡayJ6 → αxNΜcC → ΝoKΟlO → uo2ιlg → ηE2ιΧ6 → ηαΗSB6 → αΞdvMC → ΝrHΣiO → Αo8γla → ΤQ2ιΚI → ηΑiqZ6 → αR7δΙC → ΦΝgsNG → ΕpBΩkW → ΝY4ηΒO → γoSΗlA → Ρe2ιvK → ηwGΤd6 → αΓIΡXC → ΝyUΕbO → oaMΝzm → qP1κΛk → ιl5ζo4 → εα2ιB8 → ηΦΝMF6 → αΖpjUC → Νb5ζyO → αoMΝlC → Νq2ιjO → ηo6εl6 → αΨ2ιDC → ηΝΙQN6 → αphrkC → ΝA4ηβO → γΠnlKA → Ρv1κeK → ιwGΤd4 → εΓIΡX8 → ΦyUΕbG → ΕaMΝzW → qYOΛΒk → mT5ζΗo → αd1κwC → ιΝIΡN4 → εyokb8 → ΦN3θΝG → εΕokV8 → ΦZ3θΑG → εΕQΙV8 → ΦiYΑrG → ΕS8γΘW → ΤfXΒuI → ΑUEΦΖa → ΗbPΚyU → kcMΝxq → qL5ζΟk → αt5ζgC → αΝCΨNC → ΝΛokPO → ol3θom → ε31κι8 → ιζΥF64 → εΩΔVC8 → ΦΜXΒOG → ΕnTΖmW → cY0λΒy → λTLΞΗ2 → ιscwh4 → εKAαΠ8 → ΦΟueLG → ΕtFΥgW → ΕYCΨΒW → ΛYSΗΒQ → keSΗvq → eH5ζΤw → αΒHΣYC → ΝΑSΗZO → oeQΙvm → iH1κΤs → ιΒ9βY4 → εΡSΗJ8 → ΦxdvcG → ΕLHΣΟW → ΑtXΒga → UQCΨΚΗ → ΛjbxqQ → kM6εΞq → Ψr5ζiE → αΙ8γRC → ΤΝgsNI → ΑpBΩka → ΝQ4ηΚO → γoiqlA → Ρ82ιδK → ηΥvdG6 → αΔHΣWC → ΝΑWΓZO → oWQΙΔm → iX1κΓs → ιV9βΕ4 → εΡYΑJ8 → ΦxRΘcG → ΕgKΟtW → uYCΨΒg → ΛTDΧΗQ → ΙkcwpS → gK4ηΠu → γvDΧeA → ΡΙGΤRK → ΓwgsdY → UJBΩΡΗ → ΝxbxcO → oMKΟΞm → ur1κig → ιE8γΧ4 → εΤΗSH8 → ΦΒdvYG → ΕTHΣΗW → ΑdXΒwa → UQIΡΚΗ → yjbxqc → NL6εΟΞ → ΨtpjgE → ΙD5ζΨS → αΚftQC → ΝjDΧqO → Ιo6εlS → Ψg2ιtE → ηΙCΨR6 → αΛgsPC → ΝlBΩoO → Νo2ιlO → ηo2ιl6 → ηα2ιB6 → ηαΝMB6 → αΞpjMC → Νr5ζiO → αo8γlC → ΤΝ2ιNI → ηΑokZ6 → αR3θΙC → εΝgsN8 → ΦpBΩkG → ΝΕ4ηVO → γoYΑlA → ΡS2ιΘK → ηweud6 → αJFΥΡC → ΝΕwcVO → oZJΠΑm → wR1κΙe → ιhHΣs4 → εΑAαZ8 → ΦΟQΙLG → ΕthrgW → YD9βΨΓ → ΡΚTΖQK → wjbxqe → MI6εΣΟ → ΨzrhaE → ΙP9βΛS → ΡlftoK → wE2ιΧe → ηΘHΣS6 → αΑeuZC → ΝRFΥΙO → ΕogslW → YC2ιΩΓ → ηΜTΖO6 → αnbxmC → ΝM0λΞO → λrnli2 → ι91κγ4 → ιεΡI74 → εΧxbE8 → ΦΘLΞSG → ΕseuhW → YGAαΥΓ → ΟΔTΖWM → scWΓxi → WL9βΟΕ → ΡtXΒgK → wUCΨΖe → ΛbHΣyQ → ΑkMΝpa → qQ4ηΚk → γj5ζqA → αΡ6εJC → ΨΝwcNE → ΙpJΠkS → wg4ηte → γICΨΣA → ΡΛyaPK → wlNΜoe → oI2ιΣm → ηz1κa6 → ιαOΛB4 → εΞlnM8 → Φr1κiG → ιΕ8γV4 → εΤYΑH8 → ΦΒRΘYG → ΕgSΗtW → eYCΨΒw → ΛTHΣΗQ → Αkcwpa → QK4ηΠΛ → γvjpeA → ΡH5ζΤK → αΒvdYC → ΝTHΣΗO → Αocwla → QK2ιΠΛ → ηvjpe6 → αH5ζΤC → αΝΑYNC → ΝpRΘkO → og4ηtm → γD1κΨA → ιΡΙQJ4 → εxhrc8 → ΦL9βΟG → ΡΕsgVK → wZBΩΑe → ΝRHΣΙO → Αogsla → QC2ιΩΛ → ηΜjpO6 → αn5ζmC → αΝ0λNC → λΝokN2 → ιp3θk4 → ζδ4η87 → γΨΤGDA → ΡΚΒXQK → wjTΖqe → cI6εΣy → ΨzLΞaE → ΙsOΛhS → mgAαto → ΟD1κΨM → ιΚrhQ4 → εj9βq8 → ΦΡ6εJG → ΨΕwcVE → ΙZJΠΑS → wgQΙte → iICΨΣs → Λz9βaQ → ΡkOΛpK → wm4ηne → γI0λΣA → λΡyaJ2 → ιxNΜc4 → εoKΟl8 → Φu2ιfG → ηΕEΦV6 → αΗYΑTC → ΝdRΘwO → ogIΡtm → yD1κΨc → ιΚLΞQ4 → εsiqh8 → ΦB7δαG → ΦΞΔVMG → ΕrXΒiW → YU8γΖΓ → ΤbTΖyI → ΑcMΝxa → qQKΟΚk → uj5ζqg → αE6εΧC → ΨΝΗSNE → ΙpdvkS → gI4ηΣu → γzDΧaA → ΡΙOΛRK → wmgsne → IC0λΩΤ → λΜzZO2 → ιnPΚm4 → εk0λp8 → λΦ4ηF2 → ιγΕU94 → εΣZzI8 → ΦzPΚaG → ΕkOΛpW → mY4ηΒo → γT1κΗA → ιΡcwJ4 → εxJΠc8 → ΦwKΟdG → ΕuIΡfW → yYEΦΒc → ΗTLΞΗU → sdbxwi → MJ9βΡΟ → ΡxrhcK → wL9βΟe → ΡtHΣgK → ΑwCΨda → ΛQIΡΚQ → ykiqpc → M84ηδΟ → γΥrhGA → ΡΔ9βWK → ΡwWΓdK → wWIΡΔe → yXHΣΓc → ΑVLΞΕa → sZPΚΑi → kR9βΙq → Ρh5ζsK → αwAαdC → ΟΝIΡNM → ysokhc → MB3θαΟ → εΞrhM8 → Φr9βiG → ΡΕ8γVK → ΤwYΑdI → ΑSIΡΘa → yfPΚuc → kMEΦΞq → Ηr5ζiU → αc8γxC → ΤΝKΟNI → Αuokfa → QF3θΦΛ → εΖjpU8 → Φb5ζyG → αΕMΝVC → ΝqYΑjO → oS6εΘm → Ψf1κuE → ιΙEΦR4 → εΗgsT8 → ΦdBΩwG → ΝΕIΡVO → yoYΑlc → SM2ιΞΙ → ηrfti6 → αE8γΧC → ΤΝΗSNI → Αpdvka → QI4ηΣΛ → γzjpaA → ΡP5ζΛK → αwkodC → ΝJ3θΡO → εxnlc8 → ΦL1κΟG → ιΕsgV4 → εZBΩΑ8 → ΦΝQΙNG → ΕphrkW → YA4ηβΓ → γΠTΖKA → ΡvbxeK → wMGΤΞe → ΓrHΣiY → ΑU8γΖa → ΤbPΚyI → ΑkMΝpa
745 max steps1000000 → 0μμμμμμ → λμμμμμ1 → λ0μμμλ2 → μκ0μλ21 → μλθμ311 → λλημ412 → λιζμ532 → κθγμ843 → ιζΨμC64 → θγΡμI95 → ηΨΘμRD6 → ζΣuμeI7 → εΜcμwO8 → δΕYμΑV9 → γwVμΔdA → βvPμΚeB → αΑUμΕZC → ΩuUμΕfD → ΨtOμΛgE → ΧyTμΖbF → ΦsTμΖhG → ΥrNμΜiH → ΤwSμΗdI → ΣqSμΗjJ → ΡpMμΝkK → ΠuRμΘfL → ΟoRμΘlM → ΞnLμΞmN → ΟqQμΙjM → ΞoOμΛlN → ΝpOμΛkO → ΜoPμΚlP → ΛmNμΜnQ → ΝlNμΜoO → ΝoPμΚlO → ΜnNμΜmP → ΝmOμΛnO → ΜoNμΜlP → ΝmPμΚnO → ΜnMμΝmP → ΞnOμΛmN → ΝpNμΜkO → ΝoQμΙlO → ΜmMμΝnP → ΞnOμΛmN