Base 106: Maximum Iteration Sequences: Cycle Start

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
Cycle Start
11 max steps10
22 max steps20 → 1σ → ρ3
354 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
47 max stepsD00e → eCηΕ → ΤPΣQ → tqqp → 3ττρ → ρ2ρ4 → ομ76 → ιδFC
542 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
6281 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