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 steps1 → 0 → 0
255 max steps20 → 1σ → ρ3 → ν7 → εF → ΝV → gΒ → KΩ → Γf → MΧ → yj → Eζ → ΟT → kx → Cθ → ΤP → sp → 2ς → ο5 → ιB → ΦN → wl → Aκ → ΨL → Αh → Iβ → Ηb → UΞ → iz → Gδ → ΛX → cΖ → SΠ → mv → 8μ → γH → ΙZ → YΚ → aΘ → WΜ → eΔ → OΥ → un → 6ξ → ηD → ΡR → ot → 4π → λ9 → αJ → Εd → QΣ → qr → 0τ → σ1 → ρ3
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 → qτr → qτr
433 max stepsD00e → eCηΕ → ΤPΣQ → tqqp → 3ττρ → ρ2ρ4 → ομ76 → ιδFC → ΦΜVO → wfΒm → M9κΨ → αzhK → ΕHβe → ΙPΣa → sXΚq → c1ςΗ → ρTΞ4 → νjx8 → εDζG → ΡΜVS → ofΒu → M5ξΨ → ιzhC → ΦHβO → Ιvla → Y9κΛ → αbΖK → ΕTΞe → kPΣy → sDζq → Ρ1ςS → ρnt4 → ν5ξ8 → ιδFC
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 → ΙXτΚa → ΛYτΙY → ΚbτΖZ → ΙXτΚa
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 → ΑsGγpi → ΛI2ρβY → οΘbΖa6 → ιXTΞΛC → ΦkcΕxO → wSCηΠm → Τn9κuQ → αs6νpK → ηΕ2ρdE → οΡQΡR6 → ιqosrC → Φ40σπO → σμvl82 → ρδ9κG4 → ναΛWJ8 → εΖdΔcG → ΝTPΣΟW → slfΒwq → MB1ςιΨ → ρΧzhM4 → νzHβi8 → εΙGγZG → ΝΛYΙXW → gdZΘΕΓ → YRLΧΡΛ → ΑpbΖsi → UI2ρβΟ → οΘjxa6 → ιXDζΛC → ΦΡcΕRO → wpRΠsm → oA2ρκu → οΩ5ξK6 → κθΓeCB → ΨΥNΥOM → Αwumli → IB7μιγ → εΧΘZMG → ΝzXΚiW → gcGγΖΓ → ΛTLΧΟY → ΑlbΖwi → UIAιβΟ → ΨΘjxaM → ΑXDζΛi → ΡdHβΕS → ΙoQΡta → qY4οΚs → λb1ςΗA → ραUΝJ4 → νΖhzc8 → εTHβΟG → ΝΙkwZW → gZBθΙΓ → ΦZLΧΙO → ΑwYΙli → aIAιβΙ → ΨΘXΚaM → ΑcWΛΖi → eTHβΟΕ → ΙlPΣwa → sYAιΚq → Ψb1ςΗM → ρΑUΝh4 → νiIαz8 → εΗGγbG → ΝΛUΝXW → igcΕΒΑ → SLHβΨΡ → ΙΒntga → YL5ξΨΛ → ιΒbΖgC → ΦUKΨΞO → Γwiylg → MGAιδΨ → ΨΜzhWM → ΑfHβΓi → ΙNHβΦa → ΙxXΚka → cYCηΚΗ → ΤbTΞΗQ → skUΝxq → iD1ςηΑ → ρΣHβQ4 → νΙqqZ8 → εYττΙG → δΚJΩYH → ΛΕaΗdY → cWQΡΜΗ → qfTΞΓs → kN1ςΦy → ρxDζk4 → νΡCηR8 → εΤosPG → Νt3πoW → νg4οΒ8 → λεKΨFA → αΞΒfUK → ΕjLΧye → ΑQEεΣi → ΟrHβqU → Ιk0σxa → σYCηΚ2 → ρΤaΗP4 → νtVΜo8 → εg4οΒG → λΝKΨVA → αΓgΑfK → ΕNJΩΦe → ΕxPΣke → sQCηΣq → Τr1ςqQ → ρs0σp4 → σν2ρ72 → ροεE54 → νκΞTA8 → εΩjxKG → ΝΔDζeW → ΡgOΤΒS → uoKΨto → Γ64οξg → λθLΧCA → αΥzhOK → ΕvHβme → ΙQ8λΣa → γrXΚqI → Ιc0σΖa → σYSΟΚ2 → ρmaΗv4 → νW8λΜ8 → εγeΓHG → ΝΚNΥYW → wgaΗΒm → WL9κΨΝ → αΒfΒgK → ΕMKΨΧe → ΓzPΣig → sMGγΧq → Λz1ςiY → ρcGγΖ4 → νΛSΟX8 → εmcΕvG → ΝS8λΠW → γnfΒuI → ΙM6νΧa → ηzXΚiE → ΡcGγΖS → ΛoSΟtY → mc4οΖw → λT9κΟA → βΩkwKJ → ΗΔBθec → ΦUOΤΞO → wuiynm → GA6νκε → ηΩΜVKE → ΡΔfΒeS → oPLΧΤu → Αt5ξoi → ιI4οβC → λΦΗaNA → αxVΜkK → ΕgCηΒe → ΤQKΨΣQ → Γsqqpg → M2ττρΨ → ςΧHβM3 → οΙyiZ6 → ιZFδΙC → ΦΝYΙVO → whZΘΑm → YJ9καΛ → αΖbΖcK → ΕUSΟΞe → mjPΣyw → sF9κεq → αΞ1ςUK → ρΕiyd4 → νRFδΡ8 → εΝosVG → Νh3πΑW → νgIαΒ8 → εΗKΨbG → ΝΓUΝfW → igMΦΒΑ → yLHβΨk → ΙΒDζga → ΡYKΨΚS → ΓoaΗtg → WM4οΧΝ → λzfΒiA → αMGγΧK → ΛΕyidY → cRFδΡΗ → ΝpTΞsW → kg2ρΒy → οLDζΨ6 → ιΡΑgRC → ΦpJΩsO → Εw2ρle → οQAιΣ6 → ιΨqqLC → ΦΑττgO → ΥΒJΩgP → ΕuKΨne → ΓQ6νΣg → ηrLΧqE → ΡΑ0σhS → σoIαt2 → ρΗ4οb4 → νλUΝ98 → εβhzIG → ΝΘHβaW → ΙgWΛΒa → eYKΨΚΕ → ΓbPΣΗg → sVLΧΝq → Αh1ςΑi → ρJHβα4 → νΙΕcZ8 → εZRΠΙG → ΝoYΙtW → ga4οΘΓ → λXLΧΛA → αΑcΕhK → ΕSIαΠe → ΗnPΣuc → sU6νΞq → ηj1ςyE → ρΡEεR4 → νΟosT8 → εl3πwG → νΝAιV8 → εΨgΑLG → ΝΒJΩgW → ΕgKΨΒe → ΓQKΨΣg → ΓrLΧqg → ΑM0σΧi → σzHβi2 → ρΙGγZ4 → νΛYΙX8 → εdZΘΕG → ΝYQΡΚW → qgaΗΒs → WL1ςΨΝ → ρΒfΒg4 → νMKΨΧ8 → εΓyifG → ΝNFδΦW → ΝxfΒkW → gMCηΧΓ → ΤzLΧiQ → ΑsGγpi