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 steps100
214 max steps10 → 0ν → μ1 → κ3 → ζ7ΧFΖVhtΞNplζ7
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 → nνnmνonνn
419 max stepso000 → nννn → nmno → 1ννμ → μ0μ2μι32κε74ζΦF8ΧΕVGΖYΒWZSΘΓfSΘwfGΥwΔGΥYΔUΖYbUΖΑbOΜΑnOΜon0μoμ0μ2
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 → ΕWνΔXΕWνΔX
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 → ΧhRΙtGΖhBαtWΞZBαΒOΞpRΙlOph3ιtmζC2κα8θΧΜOF6βΗmnUCΞc0μyOμpLΟl2κt3ιh4ηεBα87ΩΦΝNGEΚΕolWShY2κΓuθUCΩΗ6βΜbyPCΞmMΞoOrp1λlkκ73ιζ4ηεΧE87ΩΦΗTGEΚΕcxWShYKΠΓuvUCΩΗgΜcEΧyQΘlLΟpUtd3ιxiζKAβΡ8ΧΠveLGΖuGΥgWΔZDΨΒYΚVRΙΖSigZΑutREAβΨΛΠΙirSMtg8δuiΥEAβΨIΠΙΑZSMtgQΚuijEAβΨsΠΙ8δSMΥtfuhIΒFBαΧaΞΗQΚUOpjbyrmN82κεΟθΦqjG6βΕ6ζWCΩΞXΓNEΚqUΖkShb5ηzuβOCΩΝCΞΜnmPOpm0μomμ31λκ2λιζ643θεΨD86βΦΙRGCΞΕgtWOpYCΩΓmΜU2κΗQθlbyp6βN3ιΞCζΞpkN8Χq4θkGδΖ5ηVAβΣZΑJCΞyQΚcOpjLΟrmt82κεiθΦAβG6βΠΔWLCΞuWΔgOpXDΨΔmΚW2κΕSθhXΓt6βVBαΖCΟΝZΑONroQΚmkj71λζsκΨ8δE4ζΥΘSH8ΧΓevYGΖUGΥΗWΔcYΒyYVTLΟΘΗteazwiPIAβΤΝΠΑmnaMtQ0μΛiμkAβq2κΠ5ηL4ζβtgB8ΧΟCΩMGΜΖriVQla8δΑqΥQ4θΛIδΒjqZAΣS6ζΙKΩxfudEΚKEΧΡSΘwgteUdICΩΤyΜΑKΠaQvlPΛpglF3ιΧqζΗ4θU8δΧbyFAΣΗMΞUKxrbyjeNJ7εΣΟΧyqjcGΖM6ζΟWΩsYΒiEΚT9γΘSΣhdwtKxJBαΣeΞyIΣcOzpLΟlctN3ιΞiζqAβk8ΧΠ5ηLGβΖtgVCΞaCΩΑOΜpPΛlQmk3ιqpζ62κη8θαΦFC6βΝΕVOCΞoYΒmOpT1λΘmκe2κw4θζHΤ76βΨΑZECΞΙQΚSOpjfurmF82κεΨθΦΗTG6βΕcxWCΞYKΠΓOvpTΗlgdF3ιΧyζΗKΠU8ΧvbyfGΖNFΦΞWΖqYΒkWZT5ηΘΓβeSΘwCΞfHΤvOΒpFΦlaΖR3ιΚWζiYΒs8ΧT9γΘGΣΖdwVKxaIΣΑezQIΣΛczkMΞqcrN5ηΞkβq6ζkCΩΞ5ηNEβΚpkRCΞi4θsOδp9γlAΤΡ3ιKJζzveb8ΧOGΥΝGΖΔnmXWZW0μΕΓμYSΘΓ2κfTΗv4ζdFΦx8ΧΖJΡVGΖxZΑdWZRJΡΚΓxiSΘsefJ9γΣwΣyGΥcKΔxLΟdYtVJΡΖixaAβΑeΠQIΣΛMztjqhcNC6ζαΟΩΝqjOEΚo6ζmSΩh1λtEκΚBαR4ζΞhsN8ΧqAβkGΠΖ5ηVMβtZΑhCΞRBαΚOΞphslOpB3ιβmζΟ2κM8θΧriF6βΗ8δUCΥΞbyNIΒqMΞkarR5ηΚkβi6ζsCΩΞ9γNEΣΚpkRKxi4θseδJ9γΣAΤΡxcKJzwKΠecvNHΤΞgΒqEΧkaΘR5ηΚUβicxsCΞL9γΠOΣuolgKxE2κΨeθΙIΣS6βzfubCΞOEΧΝOΘpnmlUd40μιyμεKΠ82κΦufG4ζΕEΧW8ΧΘXΓTGΖeUΖwWbZHΤΒΑΒSOΜΙangQΚuojE0μΨsμΙ8δS2κΥfuH4ζΓEΧY8ΧΘTΗTGΖecxwWZLHΤΠΓΒuSΘgafRDΨΚwΚiGΥsSΔh9γtYΣVBαΖKΞxZΑdOpRJΡΚmxi2κseθJ9γΣ6βΣxcJCΞyKΠcOvpLΟlgtF3ιΧiζΗAβU8ΧΠbyLGΖuMΞgWrZDΨΒkΚS6ζΙSΩhfutEΚFBαΧSΞΗgtUOpcCΩymΜM2κΟQθskpi6βA4θγCδΡΝNKAΣwoleKxI2κΤeθΑIΣa6βzPΛbCΞlNΝpOqo3ιmlζ51λθ8κγΦFA4ζΡΕVK8ΧwYΒeGΖTHΤΘWΒeYΒwaTRHΤΚΙΒievsaRH9γΥΛΣΓirYKxU8δΗeΥcIΣyIΒzLΟbatRNΝΚipiAβsmΠA2κγMθΡshK6βwAβeCΠΞHΤNMΒtpkhaRC4θαΛδΝirOAΣo8δmKΥx1λdIκΒJΡZ4ζxRΙd8ΧhJΡtGΖxBαdWΞZJΡΒOxpRΙlehJ3ιΣuζyCΩc8ΧΜLΟPGΖtlohWZC2καΓθΝSΘO6βoevmCΞH1λΥOκΓolY4ζU2κΗ8θΧbyF6βΗMΞUCΞrbyjOpN7εΞmΧq2κkGθΖ5ηV6γαZΑCBΠΝQΚOMtoirmiB91λδγκΤΟLI4ζΑsha8ΧQAβΛGΠΖjqVMta6ζΑiΩQAβΛEΠΚjqRMti6ζsiΩB9γβEΣΟΙRMKxsgtieJD9γΩΤΣΛybQKxkMΞqerJ5ηΣkβy6ζcCΩΞLΟNEΚtpkhShC4θαuδΝCΩOAΣΜnmPKxm0μoeμJ1λΣ2λιxc43θεKΠ86βΦufGCΞΕEΧWOΘpXΓlUdV3ιΖyζaKΠΑ8ΧvPΛfGΖlFΦpWΖZ3ιΒWζZRΙΒ8ΧhRΙtG
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 → ΞnQνΚnOΝnLνΟnPΠpOνΜlMΟrPνΛjNΞpQνΚlOΝnNνΝnPΞnOνΜnOΝpNνΝlPΞnQνΚnO