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 steps1 → 0 → 0
229 max steps20 → 1Ρ → Ο3 → Λ7 → ΓF → mV → GΒ → kX → CΖ → sP → Sp → Mv → Yj → AΘ → wL → ah → 6Μ → ΕD → qR → Ot → Un → Iz → gb → 4Ξ → Ι9 → yJ → ed → 0Σ → Ρ1 → Ο3
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 → dΣe → dΣe
423 max steps500e → e4Νe → ΘΣΣA → Θ9ΘB → yvLK → eZhe → 7ΣΣΛ → Λ6Λ8 → ΕΒFE → qlVS → OFΒu → mVlW → HEΓΒ → ojXU → KBΖy → uddO → VΣΣm → mUmW → IFΒΑ → mhZW → G7ΚΓ → ΓlVG → mFΒW → mFΒW
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 → sRΣpQ → rQΣqR → rPΣrR → sPΣrQ → sRΣpQ
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 → ol3ΞWU → ΛKEΓx8 → ΓoceTG → mL1ΠwW → ΟbFΒg4 → Λm4ΝV8 → ΙΓGΑFA → ynjXUK → eJBΖye → ueΣΣcO → tfFΒcP → mU2ΟnW → ΝJFΒy6 → ΗmecVC → uH1ΠΑO → ΟjVlY4 → ΛGAΗΒ8 → ΓwkWLG → mbDΔgW → qG4ΝΒS → ΙlNtWA → yWEΓlK → oeEΓdU → oK0ΡxU → ΡdJxe2 → Οe0Ρd4 → ΡΛ0Ρ72 → ΡΟΓE32 → ΟΜnT64 → ΛΖJxC8 → ΓtddOG → mUΣΣmW → nkΣΣWV → ml2ΟWW → ΝGEΓΒ6 → ΗokWTC → uLDΔwO → qbVlgS → OG4ΝΒu → ΙlVlWA → yGEΓΒK → olddWU → KEΣΣΓy → Δx3ΞKF → ΛoceT8 → ΓL1ΠwG → ΟmagV4 → ΛH5ΜΑ8 → ΗΓiYFC → un9ΘUO → yWIylK → geEΓdc → o40ΡΞU → ΡΚJx82 → ΟΒddG4 → ΛkΣΣW8 → ΚlPrW9 → ΑSEΓpI → oiMuZU → YK8Ιxk → ΑdBΖeI → ui0ΡZO → ΡW8Ιl2 → ΟΑEΓH4 → ΛoiYT8 → ΓL9ΘwG → ymagVK → eH5ΜΑe → ΗiΣΣYC → ΖjNtYD → sWAΗlQ → wSEΓpM → oaMuhU → YK6Λxk → ΕdBΖeE → uq0ΡRO → ΡWOsl2 → ΟUEΓn4 → ΛoIyT8 → ΓgKwbG → mc4ΝfW → ΙG2ΟΒA → ΝykWJ6 → ΗfDΔcC → uq2ΟRO → ΝWOsl6 → ΗUEΓnC → uoIyTO → gWKwlc → cF3ΞΓg → Λn3ΞU8 → ΛΓIyF8 → ΓnfbUG → mJ3ΞyW → ΛfFΒc8 → Γm2ΟVG → ΝmGΑV6 → ΗkGΑXC → ukCΕXO → sWCΕlQ → sSEΓpQ → oSMupU → YNJxuk → eXBΖke → uCΣΣΕO → Ζt9ΘOD → ysUmPK → eTHzoe → iKΣΣwa → xhDΔaL → qc6ΛfS → ΕO2ΟtE → ΝqUmR6 → ΗPHzsC → uiSoZO → WM8Ιvm → ΑZFΒiI → mi8ΙZW → ΑG8ΙΒI → ΑlhZWI → iF7ΚΓa → Γn7ΚUG → ΓmIyVG → mgGΑbW → kG4ΝΒY → ΙlBΖWA → yuEΓNK → oeWkdU → KE0ΡΔy → ΡpddS2 → ΟMΣΣu4 → ΞvJxM5 → ΙeYidA → yA0ΡΘK → ΡxddK2 → ΟcΣΣe4 → ΞfZhc5 → Ι82ΟΚA → ΝΒxJG6 → ΗlddWC → uEΣΣΓO → Δt7ΚOF → ΓoUmTG → mLHzwW → ibFΒga → m84ΝΚW → ΙΒFΒGA → ymkWVK → eHDΔΑe → qiΣΣYS → pj7ΚYT → ΓMAΗvG → wmYiVM → aH9ΘΑi → yj7ΚYK → ΓeAΗdG → wm0ΡVM → ΡaGΑh2 → Οk6ΛX4 → ΛΕCΕD8 → ΓsqQPG → mTProW → SLFΒwq → mbNtgW → WG4ΝΒm → ΙlFΒWA → ymEΓVK → oeGΑdU → kK0ΡxY → ΡdBΖe2 → Οu0ΡN4 → ΡΛWk72 → ΟΔDΔE4 → ΛqoSR8 → ΓPLvsG → maSohW → MG6ΛΒw → ΕlZhWE → qF7ΚΓS → ΓnNtUG → mWIylW → gGEΓΒc → ol3ΞWU
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 → ycJΣxfK → yeKΣwdK → xeIΣydL → zdJΣxeJ → ygJΣxbK → yeLΣvdK → xdHΣzeL → ΑeJΣxdI → zhJΣxaJ → ygMΣubK → xcIΣyfL → zdKΣweJ → yfIΣycK → zeLΣvdJ → yeHΣzdK → ΑfKΣwcI → zgJΣxbJ → ygLΣvbK → xdJΣxeL → ycJΣxfK