Base 100: 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
252 max steps20 → 1ν → λ3η7ΨFΗVkrαDΛRitΡLuhΝPmpι5γBΟNqlε9ΤJydwfΕXczsjΦHΓZgvΙTexΑbonν1λ3
352 max steps100 → 0ξξ → νξ1 → μξ2 → λξ3 → κξ4 → ιξ5 → θξ6 → ηξ7 → ζξ8 → εξ9 → δξA → γξB → βξC → αξD → ΩξE → ΨξF → ΧξG → ΦξH → ΥξI → ΤξJ → ΣξK → ΡξL → ΠξM → ΟξN → ΞξO → ΝξP → ΜξQ → ΛξR → ΚξS → ΙξT → ΘξU → ΗξV → ΖξW → ΕξX → ΔξY → ΓξZ → Βξa → Αξb → zξc → yξd → xξe → wξf → vξg → uξh → tξi → sξj → rξk → qξl → pξm → oξn → nξonξo
420 max steps300M → M2λΡ → ιth6 → γBβC → ΠΝON → snnk → 7ξξη → η6η8 → αΧFE → ΛΖVS → iZΒuSBβΛΟhtOqBβmΟ3κOηpl8Ψ3κGηΖV8ΨZΒGΗRΚWiZΒu
543 max steps10003 → 30ξνμ → ξιξ41 → νιξ42 → μθξ53 → λζξ74 → κγξA5 → ιΨξE6 → θΣξJ7 → ηΜξP8 → ζΕξW9 → εwξeA → δnξnB → γdξxC → βmξoD → αcξyE → ΩlξpF → ΨbξzG → ΧkξqH → ΦaξΑI → ΥjξrJ → ΤZξΒK → ΣiξsL → ΡYξΓM → ΠhξtN → ΟXξΔO → ΞgξuP → ΝWξΕQ → ΜfξvR → ΛVξΖS → ΚeξwT → ΙUξΗU → ΘdξxV → ΗTξΘW → ΙaξΑU → ΘXξΔV → ΗZξΒW → ΖWξΕX → ΖXξΔX → ΕXξΔY → ΕVξΖYΗWξΕWΖZξΒXΕVξΖY
6422 max steps1000IZ → ZI0νΥΔ → νΒTΘa2 → λeQΛx4 → ηkIΤr8 → ΨΑ6ηbG → αΗOΝVE → ΛoaΑnS → iQ0νΜu → νlBβq2 → λΟ4ιN4 → ηεqk98 → ΨΥ5θIG → γΗΑaVC → ΟbPΜΑO → qmOΝpm → o42λκo → ιεξξ86 → θζ3κ87 → ηαΦGD8 → ΨΜΔXQG → ΗlVΖqW → bZ4ιΓΒ → εTPΜΙA → ΤmewpK → yI2λΥe → ιΒJΣa6 → γyQΛdC → ΟkKΡrO → wq6ηlg → αG4ιΧE → εΛΕWRA → ΤjXΔsK → yW8εΖe → ΦZJΣΓI → ΓySΙda → gSKΡΚw → whFΧug → ΗGCαΧW → ΝΖZΒWQ → mZRΚΓq → iT3κΙu → ηfBβw8 → ΨΟGΦNG → ΗΕqkXW → aX5θΕΓ → γXRΚΕC → ΟiWΕtO → qYAγΔm → ΡV3κΗM → ηuaΑh8 → ΨQCαΜG → ΝΗkqVQ → mb5θΑq → γP3κΝC → ηΟmoN8 → Ψr1μkG → λΗ6ηV4 → ηαaΑD8 → ΨΜPΜQG → ΗmkqpW → a62λθΓ → ιβRΚC6 → γΞhtOC → ΟpBβmO → Οq2λlO → ιq4ιl6 → εγ4ιBA → εΤΟMJA → ΤzrjcK → yN7ζΟe → ΨrJΣkG → Ηy6ηdW → αaKΡΒE → ΛwQΛfS → kiGΦts → ΕB7ζγY → ΨΠVΖMG → ΗtZΒiW → aSAγΚΓ → ΡhRΚuM → uiCαti → ΝCAγβQ → ΡΞlpOM → up3κmi → ηC2λβ8 → ιΨΝOF6 → γΘnnUC → ΟcξξyO → ΞzFΧcP → ΗoMΟnW → sa0νΒk → νR7ζΛ2 → λΨisF4 → ηΘ9δU8 → ΨΤcyJG → ΗzLΠcW → uaMΟΒi → sRBβΛk → Οj7ζsO → Ψq8εlG → ΦΗ4ιVI → εΓaΑZA → ΤTPΜΙK → ymewpe → KI2λΥΤ → ιΒxda6 → γRJΣΛC → ΟyisdO → qL9δΡm → Τv3κgK → ηyEΨd8 → ΨΙKΡTG → ΗwewfW → aIGΦΥΓ → ΕΒRΚaY → iWQΛΖu → kZBβΓs → ΟT7ζΙO → ΨqewlG → ΗI4ιΥW → εΒZΒaA → ΤSQΛΚK → ykgure → KE6ηΩΤ → αΚxdSE → ΛhJΣuS → yiCαte → ΝKAγΣQ → ΡxlpeM → uJ3κΤi → ηzBβc8 → ΨΟMΟNG → ΗsqkjW → a95θεΓ → γΥRΚIC → ΟΒhtaO → qRBβΛm → Οj3κsO → ηq8εl8 → ΨΦ4ιHG → εΗΓYVA → ΤbTΘΑK → yeOΝxe → oKIΤΣo → Αwξξec → zx3κed → ηMIΤΠ8 → ΨΑsibG → ΗP9δΝW → ΤnZΒoK → yS0νΚe → νhJΣu2 → λyCαd4 → ηΝKΡP8 → ΨwmofG → ΗH1μΦW → λΔZΒY4 → ηVRΚΗ8 → ΨiaΑtG → ΗQAγΜW → ΡlZΒqM → uS4ιΚi → εhBβuA → ΤΟCαNK → ΝyqkdQ → mL5θΡq → γv3κgC → ηΟEΨN8 → ΨΙqkTG → Ηf5θwW → γaGΦΒC → ΟΕQΛXO → qkWΕrm → Y73κηΕ → ηΩVΖE8 → ΨΚZΒSG → ΗhRΚuW → iaCαΒu → ΝRBβΛQ → ΟmispO → qA2λδm → ιΣ3κK6 → ηγweB8 → ΨΠHΥMG → ΗΓsiZW → aT9δΙΓ → ΤfRΚwK → yiGΦte → ΕKAγΣY → ΡxVΖeM → uaIΤΒi → ΑRBβΛc → ΟjNΞsO → rp8εml → Φ62λθI → ιβΒZC6 → γΞRΚOC → ΟphtmO → qC2λβm → ιΞ3κO6 → ηγomB8 → ΨΠ1μMG → λΗsiV4 → ηb9δΑ8 → ΨΤOΝJG → ΗznncW → aMξξΟΓ → ΠΒBβaN → ΟsQΛjO → qk8εrm → Φ73κηI → ηΩΒZE8 → ΨΚRΚSG → ΗigutW → aEAγΩΓ → ΡΚRΚSM → uiguti → ECAγβα → ΡΞΚROM → uphtmi → DB2λγβ → ιΠΜPM6 → γtlpiC → ΟB3κγO → ηΠplM8 → Ψt3κiGηΗAγV8ΨΡaΑLGΗvPΜgWmaEΨΒqΙR3κΛUηjdxs8ΨK8εΣGΦΗweVIΓbHΥΑaΓSOΝΚaohRΚuoiCξξαuβtTΘiDΝeAγxQΡmIΤpMΑu2λhcιOCαΞ6γΝomPCΟn1μoOλq0νl4νη4ι72λεΨE94ηΥΘTI8ΨΒdxaGΗRJΣΛWyjZΒseSK8εΣΛΦxhteIΓJBβΤaΟzRΚcOqiMΟtmsB3κγkηΠ7ζM8ΩΧsiGFΙΖ9δWUΤeYΓxKyUIΤΘeΑdJΣycyOKΡΞewpJΣmgyG2λΧeιΖJΣW6γyYΓdCΟUKΡΘOwqcylgMG4ιΧΡεΖthWAΤZBβΓKΟySΙdOqgKΡvmwF3κΨgηΘFΧU8ΨΗcyVGΗbLΠΑWuaOΝΒioRBβΛoΟiξξsOΞtLΠiPuoAγniΡC0νβMνΞthO2λpBβm4ηΟ2λN8ιΨqkF6γΘ5θUCγΟcyNCΟrLΠkOuq6ηliαC4ιβEεΞΚROAΤphtmKyC2λβeιΞJΣO6γyomdCΟL1μΡOλvplg4ηF3κΨ8ηΨΗUF8ΨΘbzUGΗdNΞyWqaKΡΒmwR3κΛgηjFΧs8ΨΗ8εVGΦΗaΑVIΓbPΜΑamSOΝΚqoh3κuoηCξξα8ζβ5θC9γΦΝOHCΟΔnnYOqUξξΗmΘpFΧmVΗc2λzWιaMΟΒ6γsQΛjCΟk8εrOΦq6ηlIαΓ4ιZEεΛSΙRAΤjfvsKyG8εΧeΦΖJΣWIΓyYΓdaUSKΡΚΙwhdxugKGCαΧΤΝΖxdWQmZJΣΓqyT3κΙeηfJΣw8ΨyGΦdGΗΕKΡXWwaWΕΒgYRFΧΛΕΗjVΖsWbZ8εΓΒΦTPΜΙIΓmewpaSI2λΥΛιΒhta6γRBβΛCΠΞisONsp9δmkΤ82λζKιΧxdG6γΖJΣWCΟyYΓdOqUKΡΘmwd3κygηLFΧΡ8ΨΗugVGΗbDΩΑWΛaOΝΒSoiQΛtokAξξγsδrXΔkBΡW6ηΖMαuYΓhEΛUCαΘSΝicytQmMAγΠqΡt3κiMηuAγh8ΨΡCαLGΝΗugVQmbDΩΑqΛP3κΝSηnhto8ΨC0νβGνΞΖVO2λpZΒm4ηS2λΚ8ιΨguF6γΘDΩUCΟΛcyROqjLΠsmu93κεiηΥBβI8ΨΟΑaNGΗrPΜkWma6ηΒqαR3κΛEηΛisR8Ψj9δsGΤΗ8εVKΦyaΑdIΓQKΡΜawlRΚqgiG4ιΧuεΖBβWAΤΟYΓNKyrTΘkeeK6ηΣyαxJΣeEΛyIΤdSΑiKΡtcwOAγΞgΡpFΧmMΗu2λhWιaCαΒ6γΝQΛPCΟnjroOq80νζmνΧ3κG2ληΕW74ηΩXΔE8ΨΚVΖSGΗhZΒuWaSCαΚΓΝhRΚuQmiCαtqΝB3κγQηΠlpM8Ψt3κiG
754 max stepsP000000 → OξξξξξΞ → ΞNξξξΞP → ΟΝNξΞPO → ΟqnξnlO → ΞT2ξλΙP → μΚjξrS3 → λΘPξΜU4 → κΚgξuS5 → ιΖSξΙW6 → θΕbξzX7 → ηySξΙd8 → ζΓUξΗZ9 → εzWξΕcA → δwRξΚfB → γΑTξΘbC → βxVξΖeD → αuQξΛhE → ΩySξΙdF → ΨvUξΗgG → ΧsPξΜjH → ΦwRξΚfI → ΥtTξΘiJ → ΤqOξΝlK → ΣuQξΛhL → ΡrSξΙkM → ΠoNξΞnN → ΟsPξΜjO → ΞpRξΚmP → ΝmMξΟpQ → ΠoPξΜnN → ΟqNξΞlO → ΟqRξΚlO → ΞnNξΞoP → ΟoPξΜnO → ΞpNξΞmPΟoQξΛnOΞoMξΟnPΠpPξΜmNΟqOξΝlOΞqQξΛlPΝnOξΝoQΞmOξΝpPΞoPξΜnPΝoNξΞnQΟnOξΝoOΞqOξΝlPΞoQξΛnPΝnMξΟoQΠoOξΝnNΟrOξΝkOΞqRξΚlPΝmNξΞpQΟnPξΜoOΞpNξΞmP