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 steps1 → 0 → 0
243 max steps20 → 1Τ → Ρ3 → Ν7 → ΕF → oV → IΒ → ib → 6Ξ → ΗD → sR → Qt → Sr → Ov → Wn → GΔ → mX → EΖ → qT → Mx → aj → 8Μ → ΓH → kZ → AΚ → yL → ch → 4Π → Λ9 → ΑJ → gd → 2Σ → Ο5 → ΙB → wN → Yl → CΘ → uP → Up → Kz → ef → 0Υ → Τ1 → Ρ3
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 → eΥf → eΥf
417 max stepsA00V → V9Κp → ΑJzK → heed → 3ΥΥΡ → Ρ2Ρ4 → ΟΜ76 → ΙΔFC → wnVO → YHΒm → kDΖa → s9ΚS → ΑPtK → gTpe → M1Σy → Ρbh4 → Ν5Ξ8 → ΙΔFC
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 → sPΥtS → uQΥsQ → tTΥpR → sPΥtS
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 → gV7Μoe → ΕJ1ΣΑG → ΡogcV4 → ΝJ3ΠΑ8 → ΝΕgcF8 → Εp3ΠUG → ΝoKyV8 → ΕeIΑfG → oi0ΤbW → ΤI6ΝΒ2 → ΡΗiaD4 → Νt7ΜQ8 → ΖΔSqGF → qnNvWU → YMGΓxm → mbDΖiY → sE6ΝΖS → ΗrPtSE → sUOupS → WQKyto → eTHΒqg → kN1Σwa → ΡZ9Κk4 → ΝΑAΙJ8 → ΕygcLG → od3ΠgW → ΝI2ΡΒ8 → ΟΕiaF6 → Ιp7ΜUC → ΕwKyNG → oeYkfW → IC0ΤΘΓ → ΤvjZO2 → ΡX9Κm4 → ΝΑEΕJ8 → ΕqgcTG → oN3ΠwW → ΝZHΒk8 → ΕkAΙZG → yoAΙVM → ycIΑhM → ic4Οhc → Λ64ΟΞA → ΛΘzJCA → ΑvfdOK → gX1Σme → ΡF1ΣΕ4 → ΡΝoU74 → ΝΖJzE8 → ΕrfdSG → oP1ΣuW → ΡVHΒo4 → ΝkIΑZ8 → ΕiAΙbG → yo6ΝVM → ΗcIΑhE → si4ΟbS → ΛQ6ΝtA → ΗΑSqJE → shNvcS → YQ4Οtm → ΛTDΖqA → ΑsMwRK → gaQsje → S91ΣΛs → ΡΒPtI4 → ΝjTpa8 → ΕM8ΛxG → ΓoaiVI → kJ7ΜΑa → Εh9ΚcG → Αo4ΟVK → ΛgIΑdA → Αi2ΡbK → Οg6Νd6 → ΙΗ2ΡDC → ΟwsQN6 → ΙZRrkC → wQAΙtO → yYSqlM → cOCΗvi → uX5ΞmQ → ΙUEΕpC → wqKyTO → eYMwlg → aD1ΣΗk → Ρt9ΚQ4 → ΝΑSqJ8 → ΕhNvcG → oY4ΟlW → ΛICΗΒA → ΑuiaPK → gV7Μoe
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 → ΒfKΥyeJ → ΑhJΥzcK → ΑgMΥwdK → zeIΥΑfL → ΒfKΥyeJ