Base 99: 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
214 max steps10 → 0ν → μ1 → κ3 → ζ7 → ΧF → ΖV → ZΒ → RΚ → ht → Bβ → ΞN → pl → 3κ → ζ7
352 max steps100 → 0νν → μν1 → λν2 → κν3 → ιν4 → θν5 → ην6 → ζν7 → εν8 → δν9 → γνA → βνB → ανC → ΩνD → ΨνE → ΧνF → ΦνG → ΥνH → ΤνI → ΣνJ → ΡνK → ΠνL → ΟνM → ΞνN → ΝνO → ΜνP → ΛνQ → ΚνR → ΙνS → ΘνT → ΗνU → ΖνV → ΕνW → ΔνX → ΓνY → ΒνZ → Ανa → zνb → yνc → xνd → wνe → vνf → uνg → tνh → sνi → rνj → qνk → pνl → oνm → nνn → mνo → nνn
419 max stepso000 → nννn → nmno → 1ννμ → μ0μ2 → μι32 → κε74 → ζΦF8 → ΧΕVG → ΖYΒW → ZSΘΓ → fSΘw → fGΥw → ΔGΥY → ΔUΖY → bUΖΑ → bOΜΑ → nOΜo → n0μo → μ0μ2
542 max steps30000 → 2νννλ → λ1νλ3 → μην52 → λζν63 → κδν84 → ιανB5 → θΦνF6 → ηΠνK7 → ζΚνQ8 → εΓνX9 → δuνfA → γlνoB → βeνvC → αkνpD → ΩdνwE → ΨjνqF → ΧcνxG → ΦiνrH → ΥbνyI → ΤhνsJ → ΣaνzK → ΡgνtL → ΠZνΑM → ΟfνuN → ΞYνΒO → ΝeνvP → ΜXνΓQ → ΛdνwR → ΚWνΔS → ΙcνxT → ΘVνΕU → ΗbνyV → ΖUνΖW → ΗYνΒV → ΖXνΓW → ΕXνΓX → ΔWνΔY → ΕUνΖX → ΗXνΓV → ΖYνΒW → ΕWνΔX → ΕWνΔX
6445 max stepsG000LΤ → ΤLFΦΠJ → ΖztgbW → ZOCΩΝΓ → ΜoSΘmQ → lf1λvq → κG4θΦ4 → ζδΔW98 → ΧΤWΔIG → ΖΑWΔaW → ZXPΛΔΓ → lWSΘΕq → fY4θΓw → δUGΥΗA → ΣΔbyXK → xWMΞΕe → rYIΣΓk → zU6ζΗc → ΩcMΞyE → ΚrLΟjS → th7εti → ΧCAβαG → ΠΝΕVOM → toYΒmi → TB1λβΙ → κΟevM4 → ζsGΥi8 → ΧΔ9γXG → ΣΖVΕVK → xaYΒΑe → TQIΣΛΙ → zkevqc → NH5ηΥΟ → βΓqjYC → ΞU6ζΗO → ΩpbylE → ΚN3ιΞS → ζqgtk8 → ΧD5ηΩG → βΛΕVQC → ΞkYΒqO → pT5ηΘm → βe2κwC → θΞHΤN6 → βΒpkZC → ΞS4θΙO → δpfulA → ΣF3ιΧK → ζΗwdU8 → ΧcIΣyG → ΖzLΟbW → tZNΝΒi → pSAβΙm → Πg2κuM → θtDΨh6 → βΚBαRC → ΟΝhsON → roAβmk → Π71λζM → κΨshE4 → ζΙAβS8 → ΧΠfuLG → ΖuEΧgW → ΘZDΨΒU → ΚdRΙxS → igJΡut → xEAβΨe → ΠΙIΣSM → ztfuhc → NFBαΧΟ → ΞΗqjUO → pc6ζym → ΩM2κΟE → θΚriR6 → βi8δsC → ΥΞ9γNI → ΣΒpkZK → xS4θΙe → δgIΣuA → ΣzDΨbK → ΚxNΝdS → phJΡtm → xC2καe → θΝIΣO6 → βznmbC → ΞO0μΝO → μpnml2 → κ40μι4 → μζδ872 → κΨΤHE4 → ζΙΑZS8 → ΧgQΚuG → ΖjDΨrW → ΚZ7εΒS → ΧhRΙtG → ΖhBαtW → ΞZBαΒO → ΞpRΙlO → ph3ιtm → ζC2κα8 → θΧΜOF6 → βΗmnUC → Ξc0μyO → μpLΟl2 → κt3ιh4 → ηεBα87 → ΩΦΝNGE → ΚΕolWS → hY2κΓu → θUCΩΗ6 → βΜbyPC → ΞmMΞoO → rp1λlk → κ73ιζ4 → ηεΧE87 → ΩΦΗTGE → ΚΕcxWS → hYKΠΓu → vUCΩΗg → ΜcEΧyQ → ΘlLΟpU → td3ιxi → ζKAβΡ8 → ΧΠveLG → ΖuGΥgW → ΔZDΨΒY → ΚVRΙΖS → igZΑut → REAβΨΛ → ΠΙirSM → tg8δui → ΥEAβΨI → ΠΙΑZSM → tgQΚui → jEAβΨs → ΠΙ8δSM → ΥtfuhI → ΒFBαΧa → ΞΗQΚUO → pjbyrm → N82κεΟ → θΦqjG6 → βΕ6ζWC → ΩΞXΓNE → ΚqUΖkS → hb5ηzu → βOCΩΝC → ΞΜnmPO → pm0μom → μ31λκ2 → λιζ643 → θεΨD86 → βΦΙRGC → ΞΕgtWO → pYCΩΓm → ΜU2κΗQ → θlbyp6 → βN3ιΞC → ζΞpkN8 → Χq4θkG → δΖ5ηVA → βΣZΑJC → ΞyQΚcO → pjLΟrm → t82κεi → θΦAβG6 → βΠΔWLC → ΞuWΔgO → pXDΨΔm → ΚW2κΕS → θhXΓt6 → βVBαΖC → ΟΝZΑON → roQΚmk → j71λζs → κΨ8δE4 → ζΥΘSH8 → ΧΓevYG → ΖUGΥΗW → ΔcYΒyY → VTLΟΘΗ → teazwi → PIAβΤΝ → ΠΑmnaM → tQ0μΛi → μkAβq2 → κΠ5ηL4 → ζβtgB8 → ΧΟCΩMG → ΜΖriVQ → la8δΑq → ΥQ4θΛI → δΒjqZA → ΣS6ζΙK → ΩxfudE → ΚKEΧΡS → ΘwgteU → dICΩΤy → ΜΑKΠaQ → vlPΛpg → lF3ιΧq → ζΗ4θU8 → δΧbyFA → ΣΗMΞUK → xrbyje → NJ7εΣΟ → ΧyqjcG → ΖM6ζΟW → ΩsYΒiE → ΚT9γΘS → ΣhdwtK → xJBαΣe → ΞyIΣcO → zpLΟlc → tN3ιΞi → ζqAβk8 → ΧΠ5ηLG → βΖtgVC → ΞaCΩΑO → ΜpPΛlQ → mk3ιqp → ζ62κη8 → θαΦFC6 → βΝΕVOC → ΞoYΒmO → pT1λΘm → κe2κw4 → θζHΤ76 → βΨΑZEC → ΞΙQΚSO → pjfurm → F82κεΨ → θΦΗTG6 → βΕcxWC → ΞYKΠΓO → vpTΗlg → dF3ιΧy → ζΗKΠU8 → ΧvbyfG → ΖNFΦΞW → ΖqYΒkW → ZT5ηΘΓ → βeSΘwC → ΞfHΤvO → ΒpFΦla → ΖR3ιΚW → ζiYΒs8 → ΧT9γΘG → ΣΖdwVK → xaIΣΑe → zQIΣΛc → zkMΞqc → rN5ηΞk → βq6ζkC → ΩΞ5ηNE → βΚpkRC → Ξi4θsO → δp9γlA → ΤΡ3ιKJ → ζzveb8 → ΧOGΥΝG → ΖΔnmXW → ZW0μΕΓ → μYSΘΓ2 → κfTΗv4 → ζdFΦx8 → ΧΖJΡVG → ΖxZΑdW → ZRJΡΚΓ → xiSΘse → fJ9γΣw → ΣyGΥcK → ΔxLΟdY → tVJΡΖi → xaAβΑe → ΠQIΣΛM → ztjqhc → NC6ζαΟ → ΩΝqjOE → Κo6ζmS → Ωh1λtE → κΚBαR4 → ζΞhsN8 → ΧqAβkG → ΠΖ5ηVM → βtZΑhC → ΞRBαΚO → ΞphslO → pB3ιβm → ζΟ2κM8 → θΧriF6 → βΗ8δUC → ΥΞbyNI → ΒqMΞka → rR5ηΚk → βi6ζsC → ΩΞ9γNE → ΣΚpkRK → xi4θse → δJ9γΣA → ΤΡxcKJ → zwKΠec → vNHΤΞg → ΒqEΧka → ΘR5ηΚU → βicxsC → ΞL9γΠO → ΣuolgK → xE2κΨe → θΙIΣS6 → βzfubC → ΞOEΧΝO → ΘpnmlU → d40μιy → μεKΠ82 → κΦufG4 → ζΕEΧW8 → ΧΘXΓTG → ΖeUΖwW → bZHΤΒΑ → ΒSOΜΙa → ngQΚuo → jE0μΨs → μΙ8δS2 → κΥfuH4 → ζΓEΧY8 → ΧΘTΗTG → ΖecxwW → ZLHΤΠΓ → ΒuSΘga → fRDΨΚw → ΚiGΥsS → Δh9γtY → ΣVBαΖK → ΞxZΑdO → pRJΡΚm → xi2κse → θJ9γΣ6 → βΣxcJC → ΞyKΠcO → vpLΟlg → tF3ιΧi → ζΗAβU8 → ΧΠbyLG → ΖuMΞgW → rZDΨΒk → ΚS6ζΙS → ΩhfutE → ΚFBαΧS → ΞΗgtUO → pcCΩym → ΜM2κΟQ → θskpi6 → βA4θγC → δΡΝNKA → ΣwoleK → xI2κΤe → θΑIΣa6 → βzPΛbC → ΞlNΝpO → qo3ιml → ζ51λθ8 → κγΦFA4 → ζΡΕVK8 → ΧwYΒeG → ΖTHΤΘW → ΒeYΒwa → TRHΤΚΙ → Βievsa → RH9γΥΛ → ΣΓirYK → xU8δΗe → ΥcIΣyI → ΒzLΟba → tRNΝΚi → piAβsm → ΠA2κγM → θΡshK6 → βwAβeC → ΠΞHΤNM → Βtpkha → RC4θαΛ → δΝirOA → Σo8δmK → Υx1λdI → κΒJΡZ4 → ζxRΙd8 → ΧhJΡtG → ΖxBαdW → ΞZJΡΒO → xpRΙle → hJ3ιΣu → ζyCΩc8 → ΧΜLΟPG → ΖtlohW → ZC2καΓ → θΝSΘO6 → βoevmC → ΞH1λΥO → κΓolY4 → ζU2κΗ8 → θΧbyF6 → βΗMΞUC → ΞrbyjO → pN7εΞm → Χq2κkG → θΖ5ηV6 → γαZΑCB → ΠΝQΚOM → toirmi → B91λδγ → κΤΟLI4 → ζΑsha8 → ΧQAβΛG → ΠΖjqVM → ta6ζΑi → ΩQAβΛE → ΠΚjqRM → ti6ζsi → ΩB9γβE → ΣΟΙRMK → xsgtie → JD9γΩΤ → ΣΛybQK → xkMΞqe → rJ5ηΣk → βy6ζcC → ΩΞLΟNE → ΚtpkhS → hC4θαu → δΝCΩOA → ΣΜnmPK → xm0μoe → μJ1λΣ2 → λιxc43 → θεKΠ86 → βΦufGC → ΞΕEΧWO → ΘpXΓlU → dV3ιΖy → ζaKΠΑ8 → ΧvPΛfG → ΖlFΦpW → ΖZ3ιΒW → ζZRΙΒ8 → ΧhRΙtG
759 max steps1000033 → 330νμκλ → νιην541 → μιγν942 → λθΨνD53 → κζΣνI74 → ιγΛνPA5 → θΨΑνZE6 → ηΣmνnJ7 → ζΜUνΖP8 → εΕgνtW9 → δwNνΝeA → γΕXνΓWB → βuWνΔgC → αtMνΞhD → ΩΓVνΕYE → ΨsVνΕiF → ΧrLνΟjG → ΦΑUνΖaH → ΥqUνΖkI → ΤpKνΠlJ → ΣyTνΗcK → ΡoTνΗmL → ΠnJνΡnM → ΣuRνΙgK → ΡqRνΙkL → ΠpNνΝlM → ΟsQνΚiN → ΞoQνΚmO → ΝnMνΞnP → ΟoOνΜmN → ΞqOνΜkO → ΝpQνΚlP → ΜmNνΝoQ → ΞmOνΜoO → ΝpOνΜlP → ΝnPνΛnP → ΜnMνΞnQ → ΟnNνΝnN → ΞrOνΜjO → ΝpRνΙlP → ΜlMνΞpQ → ΟnPνΛnN → ΞpMνΞlO → ΟpRνΙlN → ΞnMνΞnO → ΟpPνΛlN → ΞpOνΜlO → ΝpPνΛlP → ΜnOνΜnQ → ΝlNνΝpP → ΞnQνΚnO → ΝnLνΟnP → ΠpOνΜlM → ΟrPνΛjN → ΞpQνΚlO → ΝnNνΝnP → ΞnOνΜnO → ΝpNνΝlP → ΞnQνΚnO