Base 74: Maximum Iteration Sequences: Cycle Start

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
Cycle Start
11 max steps10
22 max steps20 → 1Λ → Ι3
338 max steps100 → 0ΜΜ → ΛΜ1 → ΚΜ2 → ΙΜ3 → ΘΜ4 → ΗΜ5 → ΖΜ6 → ΕΜ7 → ΔΜ8 → ΓΜ9 → ΒΜA → ΑΜB → zΜC → yΜD → xΜE → wΜF → vΜG → uΜH → tΜI → sΜJ → rΜK → qΜL → pΜM → oΜN → nΜO → mΜP → lΜQ → kΜR → jΜS → iΜT → hΜU → gΜV → fΜW → eΜX → dΜY → cΜZ → bΜa → aΜb
47 max steps900S → S8Γk → uHtI → daaZ → 3ΜΜΙ → Ι2Ι4 → ΗΔ76 → ΑvFC
531 max stepsa0000 → ZΜΜΜc → cYΜca → d1ΜΚZ → ΛZΜb2 → ΚaΜa3 → ΙYΜc4 → ΘZΜb5 → ΗXΜd6 → ΖYΜc7 → ΕWΜe8 → ΔXΜd9 → ΓVΜfA → ΒWΜeB → ΑUΜgC → zVΜfD → yTΜhE → xUΜgF → wSΜiG → vTΜhH → uRΜjI → tSΜiJ → sQΜkK → rRΜjL → qPΜlM → pQΜkN → oOΜmO → nPΜlP → mNΜnQ → oMΜoO → pPΜlN → oPΜlO
6320 max stepsQ000oo → ooPlNO → RQLpll → ULJrqi → YVDxge → kB5ΖΑS → ΑpHtMC → ocSiZO → QG2Ιvm → ΗfLpW6 → ΑU8ΓhC → uoCyNI → mcQkZQ → MK2Ιrq → ΗXThe6 → ΑE6ΕxC → yoiSNE → kRFvkS → gJHtsW → cZ9Βca → s31ΚΙK → ΙΖXd64 → Εz5ΖC8 → ΑwmOFC → ohNnUO → RPCyml → mNJroQ → YRLpke → UJ5Ζsi → ΑZDxcC → ok2ΙRO → ΗQIsl6 → ΑaKqbC → oW0ΛfO → ΛQ8Γl2 → ΙuKqH4 → ΕdVfY8 → wA4ΗΒG → ΓrfVKA → sX9ΒeK → sY6ΕdK → yY4ΗdE → Γk4ΗRA → ΓsIsJA → saYcbK → Y40ΛΘe → ΛΔ5Ζ82 → ΙΑuGB4 → ΕpdXM8 → wT5ΖiG → ΑgEwVC → oiAΑTO → qQEwlM → iUKqhU → WECyxg → mj9ΒSQ → sMGupK → eYSidY → G64ΗΖw → ΓzfVCA → sn9ΒOK → sYOmdK → YO4Ηne → ΓP5ΖmA → ΑsMoJC → oZRjcO → QI2Ιtm → ΗbLpa6 → ΑU0ΛhC → ΛoCyN2 → ΙmQkP4 → ΕNJro8 → wYQkdG → gK4ΗrW → ΓX9ΒeA → tr6ΕKJ → yaWebE → k80ΛΔS → ΛvHtG2 → ΙfbZW4 → Ε91ΚΓ8 → ΙwsIF4 → ΕhZbU8 → wD1ΚyG → ΙlfVQ4 → ΕL9Βq8 → wsUgJG → gZBzcW → oA2ΙΒO → ΗrPlK6 → ΑXLpeC → oU6ΕhO → yQCylE → mkKqRQ → WMIspg → aT9Βic → sF1ΚwK → ΙhXdU4 → ΕD5Ζy8 → ΑwkQFC → ohJrUO → YQCyle → mL5ΖqQ → ΑVLpgC → oUAΑhO → qQCylM → mUKqhQ → WMCypg → mT9ΒiQ → sMEwpK → iYSidU → GE4Ηxw → ΓjfVSA → sH9ΒuK → sdXdYK → Y64ΗΖe → Γz5ΖCA → ΑsmOJC → oZNncO → RP2Ιml → ΗNJro6 → ΑYQkdC → oK4ΗrO → ΓXPleA → sM6ΕpK → yYSidE → kG4ΗvS → ΓfHtWA → sc8ΓZK → uY2ΙdI → Ηc4ΗZ6 → ΓΑ2ΙBA → ΗsoMJ6 → ΑZRjcC → oI2ΙtO → ΗbPla6 → ΑM0ΛpC → ΛoSiN2 → ΙRFvk4 → ΕgIsV8 → waAΑbG → qg0ΛVM → ΛUAΑh2 → ΙqCyL4 → ΕmUgP8 → wNBzoG → ogQkVO → QKAΑrm → qXLpeM → VT6Εih → yFBzwE → okgURO → QJBzsm → oZLpcO → UQ2Ιli → ΗLDxq6 → ΑkUgRC → oJBzsO → oZPlcO → QM2Ιpm → ΗTLpi6 → ΑUEwhC → oiCyTO → mQEwlQ → iMKqpU → WTDxig → kF9ΒwS → shHtUK → cYCyda → m51ΚΗQ → ΙΒLpA4 → ΕrThK8 → wXDxeG → kg6ΕVS → yIAΑtE → qkaaRM → UIΜΜsi → th9ΒUJ → saCybK → mY0ΛdQ → ΛM4Ηp2 → ΙΓSi94 → ΕtFvI8 → wgaaVG → gAΜΜΑW → ΒfJrWB → qY8ΓdM → uU4ΗhI → ΓcCyZA → sm2ΙPK → ΗYMod6 → ΑS4ΗjC → ΓoGuNA → seQkXK → YK6Εre → yX5ΖeE → Αk6ΕRC → yoIsNE → kaQkbS → KI0Λts → ΛbXda2 → Ι60ΛΖ4 → ΛΕyC72 → ΙxlPE4 → ΕjLpS8 → wUGuhG → geCyXW → mA6ΕΒQ → yrLpKE → kXTheS → IE6Εxu → yjbZSE → kH1ΚuS → ΙdHtY4 → Εc4ΗZ8 → Γw2ΙFA → ΗsgUJ6 → ΑZBzcC → pn2ΙON → ΗSOmj6 → ΑOGunC → oeOmXO → QO6Εnm → yPLpmE → kUMohS → SICytk → mbHtaQ → cM0Λpa → ΛT1Κi2 → ΚΘEw43 → ΗΔhT86 → ΑvDxGC → okeWRO → QJ7Δsm → wZLpcG → gU2ΙhW → ΗD9Βy6 → ΑskQJC → oZJrcO → YQ2Ιle → ΗL5Ζq6 → ΒzUgCB → qnBzOM → oUOmhO → QOCynm → mPLpmQ → UNLpoi → URDxki → kJDxsS → kZHtcS → cI2Ιta → Ηb1Κa6 → ΙΑ0ΛB4 → ΛΕoM72 → ΙxRjE4 → ΕjHtS8 → wcGuZG → ge2ΙXW → ΗA6ΕΒ6 → ΑyqKDC → olVfQO → QL9Βqm → sVLpgK → YUAΑhe → qD5ΖyM → ΑlThQC → oLDxqO → kVPlgS → MIAΑtq → qbThaM → UE0Λxi → ΛjDxS2 → ΙkGuR4 → ΕeIsX8 → wa6ΕbG → yg0ΛVE → ΛkAΑR2 → ΙqIsL4 → ΕaUgb8 → wC0ΛzG → ΛnfVO2 → ΙP9Βm4 → ΕsMoJ8 → wZRjcG → gI2ΙtW → Ηb9Βa6 → Αs0ΛJC → ΛoYcN2 → ΙR3Θk4 → ΖΔIs87 → yvZbGE → kf1ΚWS → ΙI8Γt4 → ΕuaaH8 → wcΜΜYG → vdJrYH → eY4ΗdY → Γ64ΗΖA → ΓzrJCA → snXdOK → YP5Ζme → ΑN5ΖoC → ΑoQkNC → oRJrkO → YQIsle → aL5Ζqc → ΑV1ΚgC → ΙoAΑN4 → ΕqQkL8 → wVJrgG → gYAΑdW → qA4ΗΒM → ΓrThKA → sXDxeK → kY6ΕdS → yI4ΗtE → ΓkaaRA → sIΜΜsK → tqΜΜKJ → sr2ΙKK → ΗYWed6
736 max stepsH0000ab → baGΜubb → vJΜΜΜrH → usJΜrJI → tbYΜcaJ → sL1ΜΚqK → ΛpWΜeM2 → ΚoIΜsN3 → ΙrUΜgK4 → ΘoMΜoN5 → ΗlQΜkQ6 → ΖgKΜqV7 → ΕlKΜqQ8 → ΔkPΜlR9 → ΓeJΜrXA → ΒjJΜrSB → ΑiOΜmTC → zcIΜsZD → yhIΜsUE → xgNΜnVF → waHΜtbG → vfIΜsWH → udLΜpYI → tZGΜucJ → vbJΜraH → ucGΜuZI → vcKΜqZH → ubGΜuaI → vcJΜrZH → ucHΜtZI → ucJΜrZI → tbHΜtaJ → uaIΜsbI → tcHΜtZJ → uaJΜrbI → tbGΜuaJ → vbIΜsaH