Base 88: Maximum Iteration Sequences: Full Cycle

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
Full Cycle
12 max steps100
213 max steps20 → 1α → Ψ3Τ7ΛFuVcnΕLihα1Ψ3
346 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 → hβihβi
418 max steps2009 → 91ΩΣ → ΨΘH4 → ΤpZ8 → ΛFΚG → vsWV → QLΔΑ → iZpi → FββΛ → ΛEΛG → wtVU → SNΒy → eVtm → O7ΣΓΛdlGu7ΣWΛNΒGudlWO7ΣΓ
538 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 → wRβxUySβwSxVβtTwRβxU
6588 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 → Λr7ΣYGΛuIΗVGuoOΑbWcOCΝΒoΑdBΞmQΓa8ΡpOΙeEΛlIwq6ΤZUΝSGΙxEysUuXSWQKΕzukZNΒqgeH3ΧΙmΤr7ΣY8ΜΚIΗGFwtnbWUSNBΞΓyΓfVtkOeO4ΦΒmΡd7ΣmAΛΗ8ΡJGΙumcVIqP9ΠΑaΗbFΚoKumCΝdWΑO8ΡΒQΙdZpmIqG8ΡΚaΙtFΚWIuqMΓZWgOGΙΒksd3ΧmYΤK8ΡΖ8ΛΙkeHGur5ΥYWΟOIΗΒCΓocmbOeD9ΠΝmΗz7ΣQKΛmYqdGuI8ΡΘWΙpNΒaIqeEΛlawG6ΤΚUΝtRxWEyWMΓtSgWMΓtkgN3ΧΓkΤf3Χk8ΤΛ4ΦF8ΡΛuUFAΗvPzUKmaQypeYF7ΣΛsΛvJΖUGumQydWYO8ΡΒsΙdJΖmIqm8ΡdaΙG8ΡΚIΙtpZWIqNFΚΓaufFΚkWuO4ΦΒWΡdNΒmAΗe8ΡlKΙm6ΤdIΝq8ΡZEΙyGΙRIsqWsZYMKGΙΖΕslhheYK6ββΤΗΥΖBΞK7ΝΓkeNEyf5ΥkSΟW4ΦtCΡΓMΓNAΗgekjKm62ΨΥeΦΞ7ΣC6ΟΛΑOFCΓvbnUOeRBΞymΓX7ΣsOΛeKΕlGuk6ΤfWΝO4ΦΒEΡycmRAΗX9ΠsKΗmKΕdKmk8ΡfeΙ84ΦΣIΡΚpZGAΗtFΚWKumMΓdWgO8ΡΒkΙd3ΧmIΤq8ΡZ8ΛΙGΙHGusqYXWOLHΘΕΓqjdlgaG82ΨΣΛΦΚtVG6ΟtNΒWCΓeMΓlOge6ΤlkΝ73ΧΤEΤΜxRE8ΛxVtSGuVNΒuWePNΒΑmeb7ΣomΛD7ΣΝGΛztVQGuZNΒqWeOGΙΒmsd7ΣmYΛK8ΡΖGΙukeVIqP5ΥΑaΟbFΚoCΓuCΝVOΑeOΑlQca6ΤpoΝFBΞΛEΓyuUROeXPzsmaL7ΣΕqΛjFΚgGvt2ΨWVΦQMΓz6ΟgYqjCΓI2ΨΘOΦpdla6ΟF7ΣΛCΛΓuUNGufPzkWaO4ΦΒqΡdFΚmAΗu8ΡVKΙmOΑdIqc8ΡnaΙGAΟΚIΕtpZWMiNFΚΓiueββkWtl9ΠeXΗM6ΤΔKΝmgidEy91ΩΡSΨΘVtI4ΤpNΒa8ΛeEΛlGwu6ΤVUΝSOΑxEycUunSWQAΟzuΕZNΒqMieGΙlis6ββΤYΥrPzY7ΝaIΗpEyoEΛbSwWCΝtUΑSMΓxQgaUupkQF3ΧΛΑΤvZpU8ΛRFΚyGvtWsWVQNLΔΓΑifZpkiG4ββΦΛΧΚ9ΠG5ΡΗsWJAΗnLΔcKmiAΟheΕ80αΣMαΚhhG2ΨsββW4ΧtTvW5ΡSMΓxAΗgUujKmQ2ΨzeΦZ7Σq6ΟΛGΙFCΓvrXUOeRJΖymmX7ΣseΛL7ΣΕGΛuigVGuP1ΩΑWΨbNΒo4ΤeCΝl8ΛΑ6ΤPGΝuaoVEyPDΜΑSybVtoSWOCΝΒuΑdNΒmQea8ΡpmΙF7ΣΛIΛvpZUGuRFΚyWuXNΒsWeOKΕΒmkd7ΣmgΛ93ΧΡGΤΘtVI8ΛpNΒaGueEΛlWwO6ΤΒUΝdRxmEyW8ΡtSΙWMΓtIqgMΓjagG2ΨΚkΦt3ΧW6ΤΟMΓB8ΛΔfjMGuh3ΧiWΤO0αΒ8αΛcmF2Ψv9ΠU4ΤΗQyJ8ΛnXrcGuKAΟΖWΕlNΒeMie6ΤliΝ6ββΤEΥΜ5ΥE7ΟΝwSDCΓzTvQOeZRxqmWH7ΣΙuΛrNΒYGueIΗlWoO6ΤΒcΝdBΞmEΓy8ΡROΙeWslIqM6ΤΔaΝhFΚiEyu0αVSαWOΑt2ΨcMΓn4ΤgAΟj8ΛΕ2ΨLGΦuigV6ΟP1ΩΑCΨΓaoN4ΤfDΜk8Λy4ΦRGΡuWsVAΗPLΔΑKmiaoheE80αΣΝαΚxRG2ΨtVtW4ΤOMΓΒ8ΛgcmjGuA2ΨΠWΦΖNΒK6ΟldleCΓ86ΤΣOΝΚdlGEyt7ΣWSΛWMΓtGugMΓjWgO2ΨΒkΦd3Χm6ΤΟ8ΡB8ΛΙΓMHGurfjYWOJ3ΧΗΓΤndlc8ΛB7ΣΟGΛΔtVMGuhNΒiWeO0αΒmαd7Σm2ΨΛ8ΡF4ΤΙuUH8ΛrPzYGuaIΗpWoOEΛΒcwdBΞmUΓS8ΡxOΙeUulIqQ6ΤzaΝZFΚqEyuGΙVSsWOΑtYcNJΖΓomfBΞkeΓ84ΦΣOΡΚdlGAΗt7ΣWKΛmMΓdGug8ΡjWΙO2ΨΒIΦqcmZ6ΟH9ΠΙCΗΓqYNKmfHΘkeq84ΦΣaΡΚFΚGAΗusWVKmPLΔΑeib7ΣoiΛCββΝGΞΚ1ΩGDΨΑsWP4ΤbLΔo8ΛiCΝhGΑu0αVQαaOΑp2ΨcEΛn4ΤwAΟT8ΛΕSwLGujTvgWSO2ΨΒyΦdVtm6ΟO8ΡΒCΙΓcmNIqf9ΠkaΗG4ΦΚKΡtldWAΗN7ΣΓKΛmekdGu95ΥΡWΟΘNΒICΓpdlaOeF7ΣΛmΛv7ΣUGΛuQyVGuYOΑrWcOIΗΒoodBΞmcΓC8ΡΞOΙΒdlOIqd7ΣmaΛG8ΡΚGΙusWVIqPLΔΑaibFΚoiuCββΝWΞtHΘWDΑqMΓZQgaGΙpksF3ΧΛYΤvJΖU8ΛmQydGuY8ΡrWΙOIΗΒIqocmbaGD9ΠΝΛΗztVQKmZNΒqeeH7ΣΙmΛr7ΣYG
752 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 → ΕgLβΔjMΕiMβΓhMΔiKβΕhNΖhLβΔiLΕkLβΔfMΕiNβΒhMΔhJβΖiNΗiLβΔhKΖlLβΔeLΕkOβΑfMΔgKβΕjNΖhMβΓiLΕjKβΕgMΖiNβΒhLΕiJβΖhMΗjMβΓgKΖkLβΔfLΕkNβΒfMΔhLβΔiNΕgLβΔjM