Base 80: Maximum Iteration Sequences: Full Cycle

Blog: The First Pixel: Kaprekar's Constant 6174

Radix Character Encoding
0123456789ABCDEF
GHIJKLMNOPQRSTUV
WXYZabcdefghijkl
mnopqrstuvwxyzΑΒ
ΓΔΕΖΗΘΙΚΛΜΝΞΟΠΡΣ

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
229 max steps20 → 1Ρ → Ο3Λ7ΓFmVkXsPSpMvYjwLahΕDqROtUnIzgbΙ9yJedΡ1Ο3
342 max steps100 → 0ΣΣ → ΡΣ1 → ΠΣ2 → ΟΣ3 → ΞΣ4 → ΝΣ5 → ΜΣ6 → ΛΣ7 → ΚΣ8 → ΙΣ9 → ΘΣA → ΗΣB → ΖΣC → ΕΣD → ΔΣE → ΓΣF → ΒΣG → ΑΣH → zΣI → yΣJ → xΣK → wΣL → vΣM → uΣN → tΣO → sΣP → rΣQ → qΣR → pΣS → oΣT → nΣU → mΣV → lΣW → kΣX → jΣY → iΣZ → hΣa → gΣb → fΣc → eΣd → dΣedΣe
423 max steps500e → e4Νe → ΘΣΣA → Θ9ΘB → yvLK → eZhe → 7ΣΣΛ → Λ6Λ8 → ΕΒFE → qlVS → OFΒu → mVlW → HEΓΒ → ojXU → KBΖy → uddO → VΣΣm → mUmW → IFΒΑ → mhZW → G7ΚΓ → ΓlVG → mFΒWmFΒW
537 max stepsd0000 → cΣΣΣf → fbΣfd → g1ΣΠc → ΡcΣe2 → ΠdΣd3 → ΟbΣf4 → ΞcΣe5 → ΝaΣg6 → ΜbΣf7 → ΛZΣh8 → ΚaΣg9 → ΙYΣiA → ΘZΣhB → ΗXΣjC → ΖYΣiD → ΕWΣkE → ΔXΣjF → ΓVΣlG → ΒWΣkH → ΑUΣmI → zVΣlJ → yTΣnK → xUΣmL → wSΣoM → vTΣnN → uRΣpO → tSΣoP → sQΣqQ → rRΣpR → qPΣrS → sOΣsQ → tRΣpP → sRΣpQrQΣqRrPΣrRsPΣrQsRΣpQ
6303 max stepsD000Zz → zZCΕiJ → sg8ΙbQ → ΑS4ΝpI → ΙiMuZA → yY8ΙjK → ΑeAΗdI → wi0ΡZM → Ρa8Ιh2 → ΟΑ6ΛH4 → ΛΕiYD8 → Γr9ΘQG → ymQqVK → eQGΑre → kQΣΣqY → rj5ΜYR → ΗQAΗrC → wuQqNM → aXPrki → SD7ΚΕq → ΓrNtQG → mWQqlW → QGEΓΒs → olRpWU → OKEΓxu → odVleU → KG0ΡΒy → ΡlddW2 → ΟEΣΣΓ4 → ΞΔBΖE5 → ΙuoSNA → yXLvkK → eaCΕhe → s6ΣΣΛQ → ΜrHzQ7 → ΕiQqZE → qQ8ΙrS → ΑRNtqI → iWOsla → UF7ΚΓo → ΓnJxUG → meIydW → gG0ΡΒc → Ρl3ΞW2 → ΟΛEΓ74 → ΛΔnTE8 → ΓpJxSG → meMudW → YG0ΡΒk → ΡlBΖW2 → ΟuEΓN4 → ΛoWkT8 → ΓLDΔwG → qmagVS → OH5ΜΑu → ΗjVlYC → uGAΗΒO → wlVlWM → aGEΓΒi → ol7ΚWU → ΓKEΓxG → omceVU → KH1ΠΑy → ΟjddY4 → ΛAΣΣΗ8 → ΚΘ3ΞA9 → ΛΑwKH8 → ΓjbfYG → mB3ΞΗW → ΛvFΒM8 → ΓmYiVG → mH9ΘΑW → yjFΒYK → meAΗdW → wG0ΡΒM → ΡlZhW2 → ΟF7ΚΓ4 → ΛΓmUF8 → ΓnHzUG → miIyZW → gG8ΙΒc → Αl3ΞWI → ΛiEΓZ8 → Γo8ΙTG → ΑmKwVI → icGΑfa → k82ΟΚY → ΝΒBΖG6 → ΗukWNC → uXDΔkO → qWCΕlS → sOEΓtQ → oVRpmU → OKGΑxu → kdVleY → GC0ΡΖΓ → ΡtlVO2 → ΟVFΒm4 → ΛmGΑV8 → ΓkGΑXG → mkCΕXW → sGCΕΒQ → slRpWQ → SOEΓtq → oVNtmU → WKGΑxm → kdFΒeY → mC0ΡΖW → ΡtFΒO2 → ΟmUmV4 → ΛIGΑz8 → ΓkgaXG → mD5ΜΕW → ΗrFΒQC → umQqVO → WQGΑrm → kRFΒqY → mPBΖsW → uTFΒoO → mWKwlW → cGEΓΒg → ol3ΞWUΛKEΓx8ΓoceTGmL1ΠwWΟbFΒg4Λm4ΝV8ΙΓGΑFAynjXUKeJBΖyeueΣΣcOtfFΒcPmU2ΟnWΝJFΒy6ΗmecVCuH1ΠΑOΟjVlY4ΛGAΗΒ8ΓwkWLGmbDΔgWqG4ΝΒSΙlNtWAyWEΓlKoeEΓdUoK0ΡxUΡdJxe2Οe0Ρd4ΡΛ0Ρ72ΡΟΓE32ΟΜnT64ΛΖJxC8ΓtddOGmUΣΣmWnkΣΣWVml2ΟWWΝGEΓΒ6ΗokWTCuLDΔwOqbVlgSOG4ΝΒuΙlVlWAyGEΓΒKolddWUKEΣΣΓyΔx3ΞKFΛoceT8ΓL1ΠwGΟmagV4ΛH5ΜΑ8ΗΓiYFCun9ΘUOyWIylKgeEΓdco40ΡΞUΡΚJx82ΟΒddG4ΛkΣΣW8ΚlPrW9ΑSEΓpIoiMuZUYK8ΙxkΑdBΖeIui0ΡZOΡW8Ιl2ΟΑEΓH4ΛoiYT8ΓL9ΘwGymagVKeH5ΜΑeΗiΣΣYCΖjNtYDsWAΗlQwSEΓpMoaMuhUYK6ΛxkΕdBΖeEuq0ΡROΡWOsl2ΟUEΓn4ΛoIyT8ΓgKwbGmc4ΝfWΙG2ΟΒAΝykWJ6ΗfDΔcCuq2ΟROΝWOsl6ΗUEΓnCuoIyTOgWKwlccF3ΞΓgΛn3ΞU8ΛΓIyF8ΓnfbUGmJ3ΞyWΛfFΒc8Γm2ΟVGΝmGΑV6ΗkGΑXCukCΕXOsWCΕlQsSEΓpQoSMupUYNJxukeXBΖkeuCΣΣΕOΖt9ΘODysUmPKeTHzoeiKΣΣwaxhDΔaLqc6ΛfSΕO2ΟtEΝqUmR6ΗPHzsCuiSoZOWM8ΙvmΑZFΒiImi8ΙZWΑG8ΙΒIΑlhZWIiF7ΚΓaΓn7ΚUGΓmIyVGmgGΑbWkG4ΝΒYΙlBΖWAyuEΓNKoeWkdUKE0ΡΔyΡpddS2ΟMΣΣu4ΞvJxM5ΙeYidAyA0ΡΘKΡxddK2ΟcΣΣe4ΞfZhc5Ι82ΟΚAΝΒxJG6ΗlddWCuEΣΣΓOΔt7ΚOFΓoUmTGmLHzwWibFΒgam84ΝΚWΙΒFΒGAymkWVKeHDΔΑeqiΣΣYSpj7ΚYTΓMAΗvGwmYiVMaH9ΘΑiyj7ΚYKΓeAΗdGwm0ΡVMΡaGΑh2Οk6ΛX4ΛΕCΕD8ΓsqQPGmTProWSLFΒwqmbNtgWWG4ΝΒmΙlFΒWAymEΓVKoeGΑdUkK0ΡxYΡdBΖe2Οu0ΡN4ΡΛWk72ΟΔDΔE4ΛqoSR8ΓPLvsGmaSohWMG6ΛΒwΕlZhWEqF7ΚΓSΓnNtUGmWIylWgGEΓΒcol3ΞWU
750 max steps1000000 → 0ΣΣΣΣΣΣ → ΡΣΣΣΣΣ1 → Ρ0ΣΣΣΡ2 → ΣΠ0ΣΡ21 → ΣΡΞΣ311 → ΡΡΝΣ412 → ΡΟΜΣ532 → ΠΞΙΣ843 → ΟΜΕΣC64 → ΞΙyΣI95 → ΝΕpΣRD6 → ΜzcΣeI7 → ΛtMΣuO8 → ΚoVΣlT9 → ΙgIΣybA → ΘqMΣuRB → ΗlSΣoWC → ΖeHΣzdD → ΕoLΣvTE → ΔjRΣpYF → ΓcGΣΑfG → ΒmNΣtVH → ΑeNΣtdI → zdFΣΒeJ → ΓiLΣvZG → ΒhLΣvaH → ΑgKΣwbI → zgKΣwbJ → yfKΣwcK → xeJΣxdL → ycJΣxfKyeKΣwdKxeIΣydLzdJΣxeJygJΣxbKyeLΣvdKxdHΣzeLΑeJΣxdIzhJΣxaJygMΣubKxcIΣyfLzdKΣweJyfIΣycKzeLΣvdJyeHΣzdKΑfKΣwcIzgJΣxbJygLΣvbKxdJΣxeLycJΣxfK