Base 106: 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
255 max steps20 → 1σ → ρ3ν7εFΝVΓfyjΟTkxΤPspο5ιBΦNwlΨLΑhΗbizΛXmvγHΙZunηDΡRotλ9αJΕdqrσ1ρ3
355 max steps100 → 0ττ → στ1 → ςτ2 → ρτ3 → πτ4 → οτ5 → ξτ6 → ντ7 → μτ8 → λτ9 → κτA → ιτB → θτC → ητD → ζτE → ετF → δτG → γτH → βτI → ατJ → ΩτK → ΨτL → ΧτM → ΦτN → ΥτO → ΤτP → ΣτQ → ΡτR → ΠτS → ΟτT → ΞτU → ΝτV → ΜτW → ΛτX → ΚτY → ΙτZ → Θτa → Ητb → Ζτc → Ετd → Δτe → Γτf → Βτg → Ατh → zτi → yτj → xτk → wτl → vτm → uτn → tτo → sτp → rτq → qτrqτr
433 max stepsD00e → eCηΕ → ΤPΣQ → tqqp → 3ττρ → ρ2ρ4 → ομ76 → ιδFCΦΜVOwfΒmM9κΨαzhKΕHβeΙPΣasXΚqc1ςΗρTΞ4νjx8εDζGΡΜVSofΒuM5ξΨιzhCΦHβOΙvlaY9κΛαbΖKΕTΞekPΣysDζqΡ1ςSρnt4ν5ξ8ιδFC
545 max steps10006 → 60τσο → τμτ71 → σμτ72 → ςλτ83 → ριτA4 → πζτD5 → οβτH6 → ξΦτM7 → νΟτS8 → μΘτZ9 → λzτhA → κqτqB → ιgτΑC → θpτrD → ηfτΒE → ζoτsF → εeτΓG → δnτtH → γdτΔI → βmτuJ → αcτΕK → ΩlτvL → ΨbτΖM → ΧkτwN → ΦaτΗO → ΥjτxP → ΤZτΘQ → ΣiτyR → ΡYτΙS → ΠhτzT → ΟXτΚU → ΞgτΑV → ΝWτΛW → ΜfτΒX → ΛVτΜY → ΝcτΕW → ΜZτΘX → ΛbτΖY → ΚYτΙZ → ΚZτΘZ → ΙZτΘa → ΙXτΚaΛYτΙYΚbτΖZΙXτΚa
6534 max stepsF000qβ → βqEεrJ → ΟΗ0σbU → σkUΝx2 → ρiCηz4 → νΤGγP8 → εΛsoXG → Νd3πΕW → νgQΡΒ8 → εqKΨrG → ΝΓ0σfW → σgMΦΒ2 → ρyKΨj4 → νΓEεf8 → εΟMΦTG → ΝykwjW → gFBθεΓ → ΦΞLΧUO → Αwiyli → IGAιδγ → ΨΜΘZWM → ΑfXΚΓi → cNHβΦΗ → ΙxTΞka → kYCηΚy → ΤbDζΗQ → ΡsUΝpS → oi2ρzu → οH5ξγ6 → κθΙYCB → ΨΥZΘOM → ΑvXΚmi → cI8λβΗ → γΘTΞaI → ΙkWΛxa → eYCηΚΕ → ΤbPΣΗQ → trUΝqp → i40σπΑ → σμHβ82 → ρδΘZG4 → νΜXΚW8 → εfbΖΓG → ΝUMΦΞW → yjfΒyk → MFDζεΨ → ΡΞzhUS → ojHβyu → ΙF5ξεa → ιΞXΚUC → ΦjbΖyO → wUEεΞm → Οj9κyU → αkEεxK → ΟΕCηdU → ΤkQΡxQ → sqCηrq → Τ20σςQ → σπrp42 → ρμ1ς84 → ρνγG74 → νζΚXE8 → εΠbΖSG → ΝnTΞuW → kg6νΒy → ηLDζΨE → ΣΠΑgSR → qnJΩus → Ε71ςνe → ρζPΣE4 → νΠrpS8 → εn1ςuG → ρΝ6νV4 → νηgΑD8 → εΣJΩQG → ΝΕqqdW → gQττΡΓ → ΣΒDζgR → ΡqKΨrS → Γo0σtg → σM4οΧ2 → ρλyi94 → νβFδI8 → εΝΗaVG → ΝhVΜΑW → hfIαΓΒ → ΗNJΩΦc → ΕxTΞke → kQCηΣy → ΤrDζqQ → Ρs0σpS → σo2ρt2 → ρο4ο54 → νλιA98 → εβΧLIG → ΝΘzhaW → gXHβΛΓ → ΙdLΧΕa → ΑYQΡΚi → qbHβΗs → ΙV1ςΝa → ρhXΚΑ4 → νcIαΖ8 → εΗSΟbG → ΝmUΝvW → ig8λΒΑ → γLHβΨI → ΚΘΑgaZ → aXJΩΛΙ → ΕdXΚΕe → cRPΣΡΗ → spTΞsq → k31ςρy → ρξDζ64 → νθΠRC8 → εΥntOG → Νv5ξmW → ιg8λΒC → γΦKΨNI → ΙΓwkfa → YNBθΦΛ → ΦxbΖkO → wUCηΞm → Τj9κyQ → αsEεpK → ΟΕ2ρdU → οkQΡx6 → ιqCηrC → ΦΤ0σPO → σwsol2 → ρB3πι4 → ξμΦM87 → ηδxjGE → ΡΜDζWS → ΡoeΓtS → oO4οΥu → λv5ξmA → ια8λJC → γΦΕcNI → ΙxRΠka → oYCηΚu → Τb5ξΗQ → ιsUΝpC → Φi2ρzO → οwGγl6 → ιΛAιXC → ΨΦcΕNM → ΑxRΠki → oICηβu → ΤΘ5ξaQ → ιsWΛpC → Φe2ρΔO → οwOΤl6 → ιuAιnC → ΨΦ6νNM → ηΑwkhE → ΡJBθαS → ΦΖntcO → wT5ξΟm → ιl9κwC → αΦAιNK → ΨΕwkdM → ΑRBθΡi → ΦpHβsO → Ιw2ρla → οYAιΚ6 → ιΨaΗLC → ΦΒVΜgO → wgKΨΒm → ΓL9κΨg → αΒLΧgK → ΕΑKΨhe → ΓQIαΣg → ΗrLΧqc → ΑU0σΞi → σjHβy2 → ρΙEεZ4 → νΟYΙT8 → εlZΘwG → ΝYAιΚW → ΨgaΗΒM → ΑWKΨΜi → ΓfHβΓg → ΙNLΧΦa → ΑxXΚki → cICηβΗ → ΤΘTΞaQ → skWΛxq → eD1ςηΕ → ρΣPΣQ4 → νsqqp8 → ε2ττρG → ςδBθG3 → οΦΛWN6 → ιxdΔkC → ΦQCηΣO → ΤwqqlQ → sAττιq → κrdΔqB → ΨQ0σΣM → σΑqqh2 → ρIττα4 → πβFδI5 → λΝΗaVA → αhVΜΑK → ΕgIαΒe → ΗQKΨΣc → ΓrTΞqg → kM0σΧy → σzDζi2 → ρΡGγR4 → νΛosX8 → εd3πΕG → νΝQΡV8 → εqgΑrG → ΝK0σΩW → σΔfΒe2 → ρPLΧΤ4 → νΑsoh8 → εJ3παG → νΝΕcV8 → εhRΠΑG → ΝoIαtW → Ηg4οΒc → λUKΨΞA → αΓiyfK → ΕNFδΦe → ΝxPΣkW → sgCηΒq → ΤL1ςΨQ → ρΒrpg4 → νL1ςΨ8 → ρεΑgF4 → νΞJΩU8 → εΕiydG → ΝRFδΡW → ΝpfΒsW → gM2ρΧΓ → οzLΧi6 → ιΑGγhC → ΦΛIαXO → ΗwcΕlc → USAιΠΟ → ΨnjxuM → ΑE6νζi → ηΠHβSE → ΡΙmuZS → oZ7μΙu → εZ5ξΙG → ιΝYΙVC → ΦhZΘΑO → wYIαΚm → Ηb9κΗc → αVTΞΝK → ΕkgΑxe → QKCηΩΤ → ΤΔrpeQ → sP1ςΤq → ρt1ςo4 → ρν4ο74 → νλεE98 → εβΞTIG → ΝΘjxaW → gXDζΛΓ → ΡdLΧΕS → ΑoQΡti → qI4οβs → λΘ1ςaA → ραWΛJ4 → νΖdΔc8 → εTPΣΟG → ΝskwpW → gC2ρθΓ → οΥLΧO6 → ιΑumhC → ΦJ7μαO → εΖvlcG → ΝT9κΟW → αlfΒwK → ΕMAιΧe → ΨzPΣiM → ΑsGγpiΛI2ρβYοΘbΖa6ιXTΞΛCΦkcΕxOwSCηΠmΤn9κuQαs6νpKηΕ2ρdEοΡQΡR6ιqosrCΦ40σπOσμvl82ρδ9κG4ναΛWJ8εΖdΔcGΝTPΣΟWslfΒwqMB1ςιΨρΧzhM4νzHβi8εΙGγZGΝΛYΙXWgdZΘΕΓYRLΧΡΛΑpbΖsiUI2ρβΟοΘjxa6ιXDζΛCΦΡcΕROwpRΠsmoA2ρκuοΩ5ξK6κθΓeCBΨΥNΥOMΑwumliIB7μιγεΧΘZMGΝzXΚiWgcGγΖΓΛTLΧΟYΑlbΖwiUIAιβΟΨΘjxaMΑXDζΛiΡdHβΕSΙoQΡtaqY4οΚsλb1ςΗAραUΝJ4νΖhzc8εTHβΟGΝΙkwZWgZBθΙΓΦZLΧΙOΑwYΙliaIAιβΙΨΘXΚaMΑcWΛΖieTHβΟΕΙlPΣwasYAιΚqΨb1ςΗMρΑUΝh4νiIαz8εΗGγbGΝΛUΝXWigcΕΒΑSLHβΨΡΙΒntgaYL5ξΨΛιΒbΖgCΦUKΨΞOΓwiylgMGAιδΨΨΜzhWMΑfHβΓiΙNHβΦaΙxXΚkacYCηΚΗΤbTΞΗQskUΝxqiD1ςηΑρΣHβQ4νΙqqZ8εYττΙGδΚJΩYHΛΕaΗdYcWQΡΜΗqfTΞΓskN1ςΦyρxDζk4νΡCηR8εΤosPGΝt3πoWνg4οΒ8λεKΨFAαΞΒfUKΕjLΧyeΑQEεΣiΟrHβqUΙk0σxaσYCηΚ2ρΤaΗP4νtVΜo8εg4οΒGλΝKΨVAαΓgΑfKΕNJΩΦeΕxPΣkesQCηΣqΤr1ςqQρs0σp4σν2ρ72ροεE54νκΞTA8εΩjxKGΝΔDζeWΡgOΤΒSuoKΨtoΓ64οξgλθLΧCAαΥzhOKΕvHβmeΙQ8λΣaγrXΚqIΙc0σΖaσYSΟΚ2ρmaΗv4νW8λΜ8εγeΓHGΝΚNΥYWwgaΗΒmWL9κΨΝαΒfΒgKΕMKΨΧeΓzPΣigsMGγΧqΛz1ςiYρcGγΖ4νΛSΟX8εmcΕvGΝS8λΠWγnfΒuIΙM6νΧaηzXΚiEΡcGγΖSΛoSΟtYmc4οΖwλT9κΟAβΩkwKJΗΔBθecΦUOΤΞOwuiynmGA6νκεηΩΜVKEΡΔfΒeSoPLΧΤuΑt5ξoiιI4οβCλΦΗaNAαxVΜkKΕgCηΒeΤQKΨΣQΓsqqpgM2ττρΨςΧHβM3οΙyiZ6ιZFδΙCΦΝYΙVOwhZΘΑmYJ9καΛαΖbΖcKΕUSΟΞemjPΣywsF9κεqαΞ1ςUKρΕiyd4νRFδΡ8εΝosVGΝh3πΑWνgIαΒ8εΗKΨbGΝΓUΝfWigMΦΒΑyLHβΨkΙΒDζgaΡYKΨΚSΓoaΗtgWM4οΧΝλzfΒiAαMGγΧKΛΕyidYcRFδΡΗΝpTΞsWkg2ρΒyοLDζΨ6ιΡΑgRCΦpJΩsOΕw2ρleοQAιΣ6ιΨqqLCΦΑττgOΥΒJΩgPΕuKΨneΓQ6νΣgηrLΧqEΡΑ0σhSσoIαt2ρΗ4οb4νλUΝ98εβhzIGΝΘHβaWΙgWΛΒaeYKΨΚΕΓbPΣΗgsVLΧΝqΑh1ςΑiρJHβα4νΙΕcZ8εZRΠΙGΝoYΙtWga4οΘΓλXLΧΛAαΑcΕhKΕSIαΠeΗnPΣucsU6νΞqηj1ςyEρΡEεR4νΟosT8εl3πwGνΝAιV8εΨgΑLGΝΒJΩgWΕgKΨΒeΓQKΨΣgΓrLΧqgΑM0σΧiσzHβi2ρΙGγZ4νΛYΙX8εdZΘΕGΝYQΡΚWqgaΗΒsWL1ςΨΝρΒfΒg4νMKΨΧ8εΓyifGΝNFδΦWΝxfΒkWgMCηΧΓΤzLΧiQΑsGγpi