Base 82: 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
243 max steps20 → 1Τ → Ρ3Ν7ΕFoVibΗDsRQtSrOvWnmXqTMxajΓHkZyLchΛ9ΑJgdΟ5ΙBwNYluPUpKzefΤ1Ρ3
343 max steps100 → 0ΥΥ → ΤΥ1 → ΣΥ2 → ΡΥ3 → ΠΥ4 → ΟΥ5 → ΞΥ6 → ΝΥ7 → ΜΥ8 → ΛΥ9 → ΚΥA → ΙΥB → ΘΥC → ΗΥD → ΖΥE → ΕΥF → ΔΥG → ΓΥH → ΒΥI → ΑΥJ → zΥK → yΥL → xΥM → wΥN → vΥO → uΥP → tΥQ → sΥR → rΥS → qΥT → pΥU → oΥV → nΥW → mΥX → lΥY → kΥZ → jΥa → iΥb → hΥc → gΥd → fΥe → eΥfeΥf
417 max stepsA00V → V9Κp → ΑJzK → heed → 3ΥΥΡ → Ρ2Ρ4 → ΟΜ76 → ΙΔFCwnVOYHΒmkDΖas9ΚSΑPtKgTpeM1ΣyΡbh4Ν5Ξ8ΙΔFC
538 max steps10000 → 0ΥΥΥΥ → ΤΥΥΥ1 → Τ0ΥΤ2 → ΥΠΥ31 → ΤΠΥ32 → ΣΟΥ43 → ΡΝΥ64 → ΠΚΥ95 → ΟΖΥD6 → ΞΑΥI7 → ΝuΥO8 → ΜnΥV9 → ΛfΥdA → ΚWΥmB → ΙcΥgC → ΘVΥnD → ΗbΥhE → ΖUΥoF → ΕaΥiG → ΔTΥpH → ΓZΥjI → ΒSΥqJ → ΑYΥkK → zRΥrL → yXΥlM → xQΥsN → wWΥmO → vPΥtP → uVΥnQ → tOΥuR → vSΥqP → uSΥqQ → tRΥrR → sRΥrS → sPΥtSuQΥsQtTΥpRsPΥtS
6355 max stepsV000tt → ttUoQR → TSJzrr → gPNvue → YV1Σom → ΡJDΖΑ4 → ΝsgcR8 → ΕR3ΠsG → ΝoQsV8 → ΕSIΑrG → oiOubW → WI6ΝΒo → ΗjHΒaE → sk8ΛZS → ΓQAΙtI → ykSqZM → cOAΙvi → yX5ΞmM → ΙcEΕhC → wq4ΟTO → ΛYMwlA → ΑaCΗjK → ug8ΛdQ → ΓU2ΡpI → ΟkKyZ6 → ΙeAΙfC → yw0ΤNM → ΤcYkh2 → ΡC4ΟΘ4 → ΝΛuO98 → ΕΒVnIG → ojHΒaW → kI8ΛΒa → Γj9ΚaI → Αk8ΛZK → ΓgAΙdI → yk2ΡZM → ΟcAΙh6 → Ιy4ΟLC → ΛwcgNA → ΑZ3ΠkK → ΝgAΙd8 → Εy2ΡLG → ΟocgV6 → ΙJ3ΠΑC → ΝwgcN8 → ΕZ3ΠkG → ΝoAΙV8 → ΕyIΑLG → oicgbW → I73ΠΝΓ → ΝΖjZE8 → Εr9ΚSG → ΑoOuVK → gWIΑne → iH1ΣΓc → Ρl5ΞY4 → ΝΙCΗB8 → ΕxtPMG → obTpiW → MI6ΝΒy → ΗjbhaE → s95ΞΛS → ΙΒPtIC → wjTpaO → YM8Λxm → ΓbDΖiI → sk6ΝZS → ΗQAΙtE → ysSqRM → cRNvsi → YR5Ξsm → ΙRDΖsC → wsQsRO → YSQsrm → SPDΖus → sVPtoS → UQIΑtq → iTLxqc → cN5Ξwi → ΙZ5ΞkC → ΙwAΙNC → ywYkNM → cZBΘki → wB5ΞΙO → ΙxXlMC → wbDΖiO → sY6ΝlS → ΗQCΗtE → usSqRQ → URNvsq → YRLxsm → cRDΖsi → sR5ΞsS → ΙRPtsC → wUQspO → YSKyrm → ePDΖug → sV1ΣoS → ΡQIΑt4 → ΝiSqb8 → ΕO6ΝvG → ΗoWmVE → sJFΔΑS → ohPtcW → UI4ΟΒq → ΛjLxaA → Αc8ΛhK → Γg4ΟdI → Λk2ΡZA → ΟΑAΙJ6 → ΙygcLC → wd3ΠgO → ΝY2Ρl8 → ΟΕCΗF6 → ΙuoUPC → wVJzoO → gYIΑle → iD1ΣΗc → Ρt5ΞQ4 → ΝΙSqB8 → ΕxNvMG → obXliW → IE6ΝΖΓ → ΗrjZSE → sP9ΚuS → ΑVPtoK → gUIΑpe → iL1Σyc → Ρd5Ξg4 → ΝΙ2ΡB8 → ΟΕwMF6 → ΙpZjUC → wL9ΚyO → ΑdXlgK → gE2ΡΖe → Οr1ΣS6 → ΡΙOuB4 → ΝxVnM8 → ΕbHΒiG → ok6ΝZW → ΗIAΙΒE → ysiaRM → cR7Μsi → ΕR5ΞsG → ΙoQsVC → wSIΑrO → iYOulc → WD5ΞΗo → ΙtHΒQC → wkSqZO → YOAΙvm → yXDΖmM → scEΕhS → qQ4ΟtU → ΛTLxqA → ΑcMwhK → ga4Οje → Λ91ΣΛA → ΡΒzJI4 → Νjfda8 → Ε91ΣΛG → ΡΒnVI4 → ΝjHΒa8 → Εk8ΛZG → ΓoAΙVI → ykIΑZM → icAΙhc → y64ΟΞM → ΛΘbhCA → Αv5ΞOK → ΙgWmdC → wG2ΡΔO → ΟnXlW6 → ΙHDΖΓC → wskYRO → YRBΘsm → wRDΖsO → sYQslS → SQCΗts → uTPtqQ → VTMwqp → aNJzwk → gZ9Κke → ΑB1ΣΙK → ΡxfdM4 → Νb1Σi8 → ΡΕ6ΝF4 → ΝΗoUD8 → ΕtJzQG → ogSqdW → OI2ΡΒw → ΟjXla6 → ΙE8ΛΖC → ΓwqSNI → kZNvka → YB9ΚΙm → ΑxDΖMK → sgaidS → Q82ΡΜu → ΟΔTpG6 → ΙnLxWC → wcGΓhO → mY4ΟlY → ΛECΗΖA → ΑuqSPK → gVNvoe → YJ1ΣΑm → ΡhDΖc4 → Νs4ΟR8 → ΛΕQsFA → ΑpRrUK → gQKyte → eT1Σqg → ΡN1Σw4 → ΡΝYk74 → ΝΖBΘE8 → ΕwqSNG → oZNvkW → YIAΙΒm → yjDΖaM → sc8ΛhS → ΓQ4ΟtI → ΛkSqZA → ΑOAΙvK → ygWmdM → cG2ΡΔi → Οn5ΞW6 → ΚΘGΓCB → yvlXOM → cXDΖmi → sF5ΞΕS → ΙpPtUC → wUKypO → eYKylg → eD1ΣΗg → Ρt1ΣQ4 → ΡΝSq74 → ΝΖNvE8 → ΕrXlSG → oPDΖuW → sVHΒoS → kQIΑta → iT9Κqc → ΑN5ΞwK → ΙgYkdC → wC2ΡΘO → ΟvXlO6 → ΙXDΖmC → wsEΕRO → qYQslU → SMCΗxs → ubPtiQ → VT6Νqp → ΗNJzwE → sgYkdS → QC2ΡΘu → ΟvTpO6 → ΙXLxmC → wcEΕhO → qY4ΟlU → ΛMCΗxA → ΑuaiPK → gV7ΜoeΕJ1ΣΑGΡogcV4ΝJ3ΠΑ8ΝΕgcF8Εp3ΠUGΝoKyV8ΕeIΑfGoi0ΤbWΤI6ΝΒ2ΡΗiaD4Νt7ΜQ8ΖΔSqGFqnNvWUYMGΓxmmbDΖiYsE6ΝΖSΗrPtSEsUOupSWQKytoeTHΒqgkN1ΣwaΡZ9Κk4ΝΑAΙJ8ΕygcLGod3ΠgWΝI2ΡΒ8ΟΕiaF6Ιp7ΜUCΕwKyNGoeYkfWIC0ΤΘΓΤvjZO2ΡX9Κm4ΝΑEΕJ8ΕqgcTGoN3ΠwWΝZHΒk8ΕkAΙZGyoAΙVMycIΑhMic4ΟhcΛ64ΟΞAΛΘzJCAΑvfdOKgX1ΣmeΡF1ΣΕ4ΡΝoU74ΝΖJzE8ΕrfdSGoP1ΣuWΡVHΒo4ΝkIΑZ8ΕiAΙbGyo6ΝVMΗcIΑhEsi4ΟbSΛQ6ΝtAΗΑSqJEshNvcSYQ4ΟtmΛTDΖqAΑsMwRKgaQsjeS91ΣΛsΡΒPtI4ΝjTpa8ΕM8ΛxGΓoaiVIkJ7ΜΑaΕh9ΚcGΑo4ΟVKΛgIΑdAΑi2ΡbKΟg6Νd6ΙΗ2ΡDCΟwsQN6ΙZRrkCwQAΙtOyYSqlMcOCΗviuX5ΞmQΙUEΕpCwqKyTOeYMwlgaD1ΣΗkΡt9ΚQ4ΝΑSqJ8ΕhNvcGoY4ΟlWΛICΗΒAΑuiaPKgV7Μoe
740 max steps600000e → e5ΥΥΥΞg → ΟfcΥge6 → Ξc1ΥΣh7 → ΤΛaΥi92 → ΣΚZΥjA3 → ΡΘZΥjC4 → ΠΕXΥlF5 → ΟΑWΥmJ6 → ΞvTΥpO7 → ΝpRΥrU8 → ΜlMΥwY9 → ΛpNΥvUA → ΚnQΥsWB → ΙjLΥxaC → ΘnMΥwWD → ΗlPΥtYE → ΖhKΥycF → ΕlLΥxYG → ΔjOΥuaH → ΓfJΥzeI → ΒjKΥyaJ → ΑhNΥvcK → zdIΥΑgL → ΒfLΥxeJ → ΑgIΥΑdK → ΒgMΥwdJ → ΑfIΥΑeK → ΒgLΥxdJ → ΑgJΥzdK → ΑgLΥxdK → zfJΥzeL → ΑeKΥyfK → zgJΥzdL → ΑeLΥxfK → zfIΥΑeL → ΒfKΥyeJΑhJΥzcKΑgMΥwdKzeIΥΑfLΒfKΥyeJ