Base 88: Maximum Iteration Sequences: Cycle Start

Blog: The First Pixel: Kaprekar's Constant 6174

Radix Character Encoding
0123456789ABCDEF
GHIJKLMNOPQRSTUV
WXYZabcdefghijkl
mnopqrstuvwxyzΑΒ
ΓΔΕΖΗΘΙΚΛΜΝΞΟΠΡΣ
ΤΥΦΧΨΩαβγδεζηθικ

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 → 1α → Ψ3
345 max steps100 → 0ββ → αβ1 → Ωβ2 → Ψβ3 → Χβ4 → Φβ5 → Υβ6 → Τβ7 → Σβ8 → Ρβ9 → ΠβA → ΟβB → ΞβC → ΝβD → ΜβE → ΛβF → ΚβG → ΙβH → ΘβI → ΗβJ → ΖβK → ΕβL → ΔβM → ΓβN → ΒβO → ΑβP → zβQ → yβR → xβS → wβT → vβU → uβV → tβW → sβX → rβY → qβZ → pβa → oβb → nβc → mβd → lβe → kβf → jβg → iβh → hβi
413 max steps2009 → 91ΩΣ → ΨΘH4 → ΤpZ8 → ΛFΚG → vsWV → QLΔΑ → iZpi → FββΛ → ΛEΛG → wtVU → SNΒy → eVtm → O7ΣΓ
535 max steps10005 → 50βαΧ → βΤβ61 → αΤβ62 → ΩΣβ73 → ΨΠβ94 → ΧΝβC5 → ΦΙβG6 → ΥΔβL7 → ΤxβR8 → ΣqβY9 → ΡiβgA → ΠZβpB → ΟfβjC → ΞYβqD → ΝeβkE → ΜXβrF → ΛdβlG → ΚWβsH → ΙcβmI → ΘVβtJ → ΗbβnK → ΖUβuL → ΕaβoM → ΔTβvN → ΓZβpO → ΒSβwP → ΑYβqQ → zRβxR → yXβrS → xQβyT → zUβuR → yUβuS → xTβvT → wTβvU → wRβxU
6226 max stepsa0000Ε → ΕZββpM → ΔqEΛZN → wgGΙjU → sS2ΨxY → ΦVJΖu6 → ΟmOΑdC → Γc8ΡnO → ΙeAΟlI → Εq6ΤZM → ΝiGΙhE → ys0αXS → αWKΕt2 → ΨkMΓf4 → Τg4Φj8 → ΡΛ2ΨFA → ΦΗuUJ6 → ΟnPzcC → ΓaAΟpO → ΕeEΛlM → wi6ΤhU → ΝS0αxE → αyUuR2 → ΨXPzs4 → ΤaKΕp8 → ΛkEΛfG → wu4ΦVU → ΡSOΑxA → ΗcUunK → mQAΟze → ΕZ7ΣqM → ΛiGΙhG → us0αXW → αOKΕΒ2 → Ψkcmf4 → ΤA4ΦΠ8 → ΡΛΕKFA → ΗvjfUK → mR3Χye → ΤX7Σs8 → ΜΚKΕGF → wtjfWU → SN3ΧΓy → ΤfVtk8 → ΛO4ΦΒG → ΡucmVA → ΗP9ΠΑK → ΗmaodK → mE8ΡΜe → Ιx7ΣSI → ΛqUuZG → uQGΙzW → sZNΒqY → eKGΙΖm → sl7ΣeY → ΛK6ΤΖG → ΝukeVE → yP5ΥΑS → ΟbVtoC → ΓOCΝΒO → ΑecmlQ → aA6ΤΠq → ΝΖFΚKE → yukeVS → WP5ΥΑu → ΟbNΒoC → ΓeCΝlO → Αe6ΤlQ → Νa6ΤpE → ΝyEΛRE → ywWsTS → WTLΔwu → iTNΒwi → eSββwm → xl9ΠeT → ΗU6ΤvK → ΝmQydE → yY8ΡrS → ΙWIΗtI → qoMΓba → gGCΝΚk → Αt3ΧWQ → ΤaMΓp8 → ΛgEΛjG → wu2ΨVU → ΦSOΑx6 → ΟcUunC → ΓQAΟzO → ΕeYqlM → iI6ΤΘi → ΝoββaE → ΜpNΒaF → weEΛlU → wS6ΤxU → ΝVRxuE → yWOΑtS → cWMΓto → gNBΞΓk → Γf3ΧkO → Τe4Φl8 → ΡΛ6ΤFA → ΝΗuUJE → ynPzcS → aWAΟtq → ΕNFΚΓM → uiekhW → O60αΥΓ → αΞdlC2 → ΨΒ7ΣO4 → ΤΛcmF8 → Λv9ΠUG → ΗuQyVK → mYOΑre → cJ7ΣΗo → ΛnBΞcG → ΓuAΟVO → ΕeOΑlM → ic6Τni → ΝAββΟE → ΠΜ1ΩEB → ΨΕwSL4 → ΤjTvg8 → ΛS2ΨxG → ΦuUuV6 → ΟQOΑzC → ΓcYqnO → eIAΟΘm → Εp7ΣaM → ΛiEΛhG → wu0αVU → αSOΑx2 → ΨcUun4 → ΤQAΟz8 → ΛΕYqLG → ujHΘgW → qO2ΨΒa → ΦdFΚm6 → Οu8ΡVC → ΙΓOΑNI → qfbnka → GC4ΦΞΛ → ΡΒtVOA → ΗdNΒmK → me8Ρle → Ι86ΤΣI → ΝΚpZGE → ytFΚWS → uWMΓtW → gOMΓΒk → gd3Χmk → Τ93ΧΡ8 → ΤΛΗIF8 → ΛvnbUG → uRBΞyW → ΓXNΒsO → fdKΕml → k95ΥΡg → ΟΘ3ΧIC → ΤΓoaN8 → ΛfDΜkG → yu4ΦVS → ΡWOΑtA → ΗcMΓnK → mgAΟje → Ε82ΨΣM → ΦΚhhG6 → ΟsββWC → ΞtLΔWD → ΑiMΓhQ → ga0αpk → αF3ΧΛ2 → ΨΤuU74 → ΤΜPzE8 → ΛxZpSG → uVFΚuW → uPNΒΑW → ebNΒom → eD7ΣΝm → Λz7ΣQG → ΛuYqVG → uPHΘΑW → qbNΒoa → eGCΝΚm → Αt7ΣWQ → ΛaMΓpG → ugEΛjW → wO2ΨΒU → ΦdRxm6 → ΟW8ΡtC → ΙΓMΓNI → qgekja → G62ΨΥΛ → ΦΞtVC6 → ΟΒNΒOC → ΓecmlO → eA6ΤΠm → ΝΖ7ΣKE → ΛykeRG → uX5ΥsW → ΟOKΕΒC → ΓkcmfO → eA4ΦΠm → ΡΖ7ΣKA → ΛΗkeJG → un5ΥcW → ΟOAΟΒC → ΕΓcmNM → if9Πki → Η4ββΦK → ΧΖDΜK5 → ΡykeRA → ΗX5ΥsK → ΟmKΕdC → Γk8ΡfO → Ιe4ΦlI → Ρq6ΤZA → ΝΗGΙJE → ysmcXS → WL9ΠΕu → ΗjNΒgK → me2Ψle → Φ86ΤΣ6 → ΟΝΙGDC → ΓzrXQO → eZJΖqm → mH7ΣΙe → Λr7ΣYG
733 max steps1000000 → 0ββββββ → αβββββ1 → α0βββα2 → βΩ0βα21 → βαΧβ311 → ααΦβ412 → αΨΥβ532 → ΩΧΡβ843 → ΨΥΝβC64 → ΧΡΗβI95 → ΦΝxβRD6 → ΥΘkβeI7 → ΤΒSβwO8 → ΣuYβqV9 → ΡmLβΔdA → ΠvPβzUB → ΟqUβuZC → ΞkKβΕfD → ΝtOβΑWE → ΜoTβvbF → ΛiJβΖhG → ΚrNβΒYH → ΙmSβwdI → ΘgIβΗjJ → ΘoPβzbJ → ΗiNβΒhK → ΖjJβΖgL → ΗkOβΑfK → ΖiKβΕhL → ΖkMβΓfL → ΕjMβΓgM → ΔiLβΔhN → ΕgLβΔjM