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 steps1 → 0 → 0
213 max steps20 → 1α → Ψ3 → Τ7 → ΛF → uV → OΒ → cn → AΠ → ΕL → ih → 0β → α1 → Ψ3
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 → hβi → hβi
418 max steps2009 → 91ΩΣ → ΨΘH4 → ΤpZ8 → ΛFΚG → vsWV → QLΔΑ → iZpi → FββΛ → ΛEΛG → wtVU → SNΒy → eVtm → O7ΣΓ → ΛdlG → u7ΣW → ΛNΒG → udlW → O7ΣΓ
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 → wRβxU → ySβwS → xVβtT → wRβxU
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 → Λr7ΣYG → ΛuIΗVG → uoOΑbW → cOCΝΒo → ΑdBΞmQ → Γa8ΡpO → ΙeEΛlI → wq6ΤZU → ΝSGΙxE → ysUuXS → WQKΕzu → kZNΒqg → eH3ΧΙm → Τr7ΣY8 → ΜΚIΗGF → wtnbWU → SNBΞΓy → ΓfVtkO → eO4ΦΒm → Ρd7ΣmA → ΛΗ8ΡJG → ΙumcVI → qP9ΠΑa → ΗbFΚoK → umCΝdW → ΑO8ΡΒQ → ΙdZpmI → qG8ΡΚa → ΙtFΚWI → uqMΓZW → gOGΙΒk → sd3ΧmY → ΤK8ΡΖ8 → ΛΙkeHG → ur5ΥYW → ΟOIΗΒC → ΓocmbO → eD9ΠΝm → Ηz7ΣQK → ΛmYqdG → uI8ΡΘW → ΙpNΒaI → qeEΛla → wG6ΤΚU → ΝtRxWE → yWMΓtS → gWMΓtk → gN3ΧΓk → Τf3Χk8 → ΤΛ4ΦF8 → ΡΛuUFA → ΗvPzUK → maQype → YF7ΣΛs → ΛvJΖUG → umQydW → YO8ΡΒs → ΙdJΖmI → qm8Ρda → ΙG8ΡΚI → ΙtpZWI → qNFΚΓa → ufFΚkW → uO4ΦΒW → ΡdNΒmA → Ηe8ΡlK → Ιm6ΤdI → Νq8ΡZE → ΙyGΙRI → sqWsZY → MKGΙΖΕ → slhheY → K6ββΤΗ → ΥΖBΞK7 → ΝΓkeNE → yf5ΥkS → ΟW4ΦtC → ΡΓMΓNA → ΗgekjK → m62ΨΥe → ΦΞ7ΣC6 → ΟΛΑOFC → ΓvbnUO → eRBΞym → ΓX7ΣsO → ΛeKΕlG → uk6ΤfW → ΝO4ΦΒE → ΡycmRA → ΗX9ΠsK → ΗmKΕdK → mk8Ρfe → Ι84ΦΣI → ΡΚpZGA → ΗtFΚWK → umMΓdW → gO8ΡΒk → Ιd3ΧmI → Τq8ΡZ8 → ΛΙGΙHG → usqYXW → OLHΘΕΓ → qjdlga → G82ΨΣΛ → ΦΚtVG6 → ΟtNΒWC → ΓeMΓlO → ge6Τlk → Ν73ΧΤE → ΤΜxRE8 → ΛxVtSG → uVNΒuW → ePNΒΑm → eb7Σom → ΛD7ΣΝG → ΛztVQG → uZNΒqW → eOGΙΒm → sd7ΣmY → ΛK8ΡΖG → ΙukeVI → qP5ΥΑa → ΟbFΚoC → ΓuCΝVO → ΑeOΑlQ → ca6Τpo → ΝFBΞΛE → ΓyuURO → eXPzsm → aL7ΣΕq → ΛjFΚgG → vt2ΨWV → ΦQMΓz6 → ΟgYqjC → ΓI2ΨΘO → Φpdla6 → ΟF7ΣΛC → ΛΓuUNG → ufPzkW → aO4ΦΒq → ΡdFΚmA → Ηu8ΡVK → ΙmOΑdI → qc8Ρna → ΙGAΟΚI → ΕtpZWM → iNFΚΓi → ueββkW → tl9ΠeX → ΗM6ΤΔK → ΝmgidE → y91ΩΡS → ΨΘVtI4 → ΤpNΒa8 → ΛeEΛlG → wu6ΤVU → ΝSOΑxE → ycUunS → WQAΟzu → ΕZNΒqM → ieGΙli → s6ββΤY → ΥrPzY7 → ΝaIΗpE → yoEΛbS → wWCΝtU → ΑSMΓxQ → gaUupk → QF3ΧΛΑ → ΤvZpU8 → ΛRFΚyG → vtWsWV → QNLΔΓΑ → ifZpki → G4ββΦΛ → ΧΚ9ΠG5 → ΡΗsWJA → ΗnLΔcK → miAΟhe → Ε80αΣM → αΚhhG2 → ΨsββW4 → ΧtTvW5 → ΡSMΓxA → ΗgUujK → mQ2Ψze → ΦZ7Σq6 → ΟΛGΙFC → ΓvrXUO → eRJΖym → mX7Σse → ΛL7ΣΕG → ΛuigVG → uP1ΩΑW → ΨbNΒo4 → ΤeCΝl8 → ΛΑ6ΤPG → ΝuaoVE → yPDΜΑS → ybVtoS → WOCΝΒu → ΑdNΒmQ → ea8Ρpm → ΙF7ΣΛI → ΛvpZUG → uRFΚyW → uXNΒsW → eOKΕΒm → kd7Σmg → Λ93ΧΡG → ΤΘtVI8 → ΛpNΒaG → ueEΛlW → wO6ΤΒU → ΝdRxmE → yW8ΡtS → ΙWMΓtI → qgMΓja → gG2ΨΚk → Φt3ΧW6 → ΤΟMΓB8 → ΛΔfjMG → uh3ΧiW → ΤO0αΒ8 → αΛcmF2 → Ψv9ΠU4 → ΤΗQyJ8 → ΛnXrcG → uKAΟΖW → ΕlNΒeM → ie6Τli → Ν6ββΤE → ΥΜ5ΥE7 → ΟΝwSDC → ΓzTvQO → eZRxqm → WH7ΣΙu → ΛrNΒYG → ueIΗlW → oO6ΤΒc → ΝdBΞmE → Γy8ΡRO → ΙeWslI → qM6ΤΔa → ΝhFΚiE → yu0αVS → αWOΑt2 → ΨcMΓn4 → ΤgAΟj8 → ΛΕ2ΨLG → ΦuigV6 → ΟP1ΩΑC → ΨΓaoN4 → ΤfDΜk8 → Λy4ΦRG → ΡuWsVA → ΗPLΔΑK → miaohe → E80αΣΝ → αΚxRG2 → ΨtVtW4 → ΤOMΓΒ8 → ΛgcmjG → uA2ΨΠW → ΦΖNΒK6 → ΟldleC → Γ86ΤΣO → ΝΚdlGE → yt7ΣWS → ΛWMΓtG → ugMΓjW → gO2ΨΒk → Φd3Χm6 → ΤΟ8ΡB8 → ΛΙΓMHG → urfjYW → OJ3ΧΗΓ → Τndlc8 → ΛB7ΣΟG → ΛΔtVMG → uhNΒiW → eO0αΒm → αd7Σm2 → ΨΛ8ΡF4 → ΤΙuUH8 → ΛrPzYG → uaIΗpW → oOEΛΒc → wdBΞmU → ΓS8ΡxO → ΙeUulI → qQ6Τza → ΝZFΚqE → yuGΙVS → sWOΑtY → cNJΖΓo → mfBΞke → Γ84ΦΣO → ΡΚdlGA → Ηt7ΣWK → ΛmMΓdG → ug8ΡjW → ΙO2ΨΒI → ΦqcmZ6 → ΟH9ΠΙC → ΗΓqYNK → mfHΘke → q84ΦΣa → ΡΚFΚGA → ΗusWVK → mPLΔΑe → ib7Σoi → ΛCββΝG → ΞΚ1ΩGD → ΨΑsWP4 → ΤbLΔo8 → ΛiCΝhG → Αu0αVQ → αaOΑp2 → ΨcEΛn4 → ΤwAΟT8 → ΛΕSwLG → ujTvgW → SO2ΨΒy → ΦdVtm6 → ΟO8ΡΒC → ΙΓcmNI → qf9Πka → ΗG4ΦΚK → ΡtldWA → ΗN7ΣΓK → ΛmekdG → u95ΥΡW → ΟΘNΒIC → ΓpdlaO → eF7ΣΛm → Λv7ΣUG → ΛuQyVG → uYOΑrW → cOIΗΒo → odBΞmc → ΓC8ΡΞO → ΙΒdlOI → qd7Σma → ΛG8ΡΚG → ΙusWVI → qPLΔΑa → ibFΚoi → uCββΝW → ΞtHΘWD → ΑqMΓZQ → gaGΙpk → sF3ΧΛY → ΤvJΖU8 → ΛmQydG → uY8ΡrW → ΙOIΗΒI → qocmba → GD9ΠΝΛ → ΗztVQK → mZNΒqe → eH7ΣΙm → Λr7ΣYG
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 → ΕgLβΔjM → ΕiMβΓhM → ΔiKβΕhN → ΖhLβΔiL → ΕkLβΔfM → ΕiNβΒhM → ΔhJβΖiN → ΗiLβΔhK → ΖlLβΔeL → ΕkOβΑfM → ΔgKβΕjN → ΖhMβΓiL → ΕjKβΕgM → ΖiNβΒhL → ΕiJβΖhM → ΗjMβΓgK → ΖkLβΔfL → ΕkNβΒfM → ΔhLβΔiN → ΕgLβΔjM