Base 90: 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
214 max steps20 → 1γ → α3 → Φ7 → ΝF → wV → QΒ → ar → GΜ → uX → MΖ → ij → 0δ → γ1 → α3
347 max steps100 → 0δδ → γδ1 → βδ2 → αδ3 → Ωδ4 → Ψδ5 → Χδ6 → Φδ7 → Υδ8 → Τδ9 → ΣδA → ΡδB → ΠδC → ΟδD → ΞδE → ΝδF → ΜδG → ΛδH → ΚδI → ΙδJ → ΘδK → ΗδL → ΖδM → ΕδN → ΔδO → ΓδP → ΒδQ → ΑδR → zδS → yδT → xδU → wδV → vδW → uδX → tδY → sδZ → rδa → qδb → pδc → oδd → nδe → mδf → lδg → kδh → jδi → iδj → iδj
419 max stepsB00Y → YAΡu → ΗLΖM → liih → 3δδα → α2α4 → ΨΥ76 → ΡΜFC → ΕvVO → gPΒm → c5Χq → ΡDΞC → ΕzRO → gXtm → M5ΧΗ → ΡjhC → Ε1βO → αfl4 → Φ5Χ8 → ΡΜFC
539 max steps10006 → 60δγΨ → δΥδ71 → γΥδ72 → βΤδ83 → αΡδA4 → ΩΞδD5 → ΨΚδH6 → ΧΕδM7 → ΦyδS8 → ΥrδZ9 → ΤjδhA → ΣaδqB → ΡgδkC → ΠZδrD → ΟfδlE → ΞYδsF → ΝeδmG → ΜXδtH → ΛdδnI → ΚWδuJ → ΙcδoK → ΘVδvL → ΗbδpM → ΖUδwN → ΕaδqO → ΔTδxP → ΓZδrQ → ΒSδyR → ΑYδsS → zRδzT → ΑVδvS → zUδwT → yUδwU → xTδxV → yRδzU → ΑUδwS → zVδvT → yTδxU → yTδxU
6466 max steps7000YΘ → ΘY6ΦtL → ΟmKΗfE → Αm6ΦfS → ΟY6ΦtE → ΟΑKΗRE → ΑmYsfS → YK6ΦΘu → ΟnLΖeE → Αk8ΤhS → ΛY2αtI → ΨsKΗZ6 → ΡmIΙfC → Εq6ΦbO → ΟgEΝlE → Αy4ΨTS → ΤYUwtA → ΙSKΗzK → omWufe → OA6ΦΣΕ → ΟΘflKE → Αn5ΧeS → ΡY8ΤtC → ΛΕKΗNI → smgkfa → I73ΩΦΛ → ΦΞrZE8 → ΝzHΚSG → wsWuZW → QOIΙΔΓ → qfbpmc → FD6ΦΟΞ → ΟΒxTQE → ΑbTxqS → YUEΝxu → yTLΖyU → kVTxwi → UR1βΑy → αZTxs4 → ΦUIΙx8 → ΝqSybG → wWEΝvW → yQOΓΒU → ebTxqo → UF9ΣΝy → ΙxTxUK → oUSyxe → WT9Σyw → ΙVPΒwK → ocQΑpe → aD9ΣΟs → ΙΒHΚQK → soaqda → IGAΡΜΛ → ΗvrZWM → kPHΚΓi → sd1βoa → αIAΡΚ4 → ΦΗqaL8 → ΝlFΜgG → xv4ΨWV → ΤSOΓzA → ΙeWunK → oO8ΤΔe → Λf9ΣmI → Ιs6ΦZK → ΟoIΙdE → ΑqAΡbS → ΗYEΝtM → ykKΗhU → mU2αxg → ΨT5Χy6 → ΣΠUwCB → ΗΔRzOM → kfXtmi → M71βΦΗ → αΞjhE4 → Φz1βS8 → αΝWuF4 → ΦxNΔU8 → ΝgSylG → wW4ΨvW → ΤQOΓΒA → ΙeaqnK → oG8ΤΜe → Λv9ΣWI → ΙsOΓZK → oeIΙne → qA8ΤΣc → ΛΘDΞKI → ΑsmeZS → YJ7ΥΙu → ΝpLΖcG → wkCΟhW → ΓQ2αΒQ → Ψcaqp6 → ΡGCΟΜC → ΕΓuWPO → gdNΔom → gB5ΧΡm → ΡΖ5ΧMC → ΡΕiiNC → ΕgδδkO → ΔlJΘgP → oe4Ψne → ΤA8ΤΣA → ΛΙΗKJI → splfca → ID5ΧΟΛ → ΡΒrZQC → ΕbHΚqO → sgEΝla → yI4ΨΚU → ΤrTxaA → ΙUGΛxK → uoSydY → WMAΡΖw → ΗjPΒiM → kc0γpi → γD1βΟ2 → βΩΑQ43 → ΨΥZr86 → ΡΜHΚGC → ΕvrZWO → gPHΚΓm → sd5Χoa → ΡIAΡΚC → ΗΕqaNM → khFΜki → w31βαW → αΧPΒ64 → ΦΠbpC8 → ΝΔDΞOG → ΑwemVS → YR7ΥΑu → ΝZLΖsG → wkIΙhW → qQ2αΒc → ΨbDΞq6 → ΡΑEΝRC → ΕyYsTO → gVJΘwm → oR5ΧΑe → ΡZ9ΣsC → ΙΕIΙNK → qogkdc → EB3ΩΡΟ → ΦΖzRM8 → ΝjXtiG → wM0γΖW → γjPΒi2 → αc0γp4 → γΦCΟ72 → αΞΒPE4 → ΦzbpS8 → ΝXDΞuG → ΑwMΕVS → iYQΑtk → aL1βΗs → αlHΚg4 → Φs4ΨZ8 → ΤΝIΙFA → ΙxpbUK → oTDΞye → ΑV9ΣwS → ΙYQΑtK → oaKΗre → mH9ΣΛg → Ιt5ΧYK → ΡoKΗdC → ΕmAΡfO → Ηg6ΦlM → Οk4ΨhE → ΤΑ2αRA → ΨΙYsJ6 → ΡpJΘcC → ΕoCΟdO → ΓgAΡlQ → Ηc4ΨpM → ΤkCΟhA → ΙΓ2αPK → Ψocod6 → ΡCAΡΠC → ΗΕΓONM → khdnki → A31βαΤ → αΧΘJ64 → ΦΠndC8 → ΝΔ9ΣOG → ΙwemVK → oR7ΥΑe → ΝZ9ΣsG → ΙwIΙVK → qoQΑdc → aEAΡΞs → ΗzHΚSM → skWuha → OI2αΚΕ → Ψrfla6 → ΡH5ΧΛC → ΡΕsYNC → ΕhJΘkO → og2αle → ΨA4ΨΣ6 → ΤΡΗKBA → ΙΖlfMK → oj5Χie → ΡA0γΣC → γΘΔNK2 → αnfle4 → Φ95ΧΤ8 → ΡΝΙIFC → ΕxpbUO → gTDΞym → ΑV5ΧwS → ΡYQΑtC → ΕaKΗrO → mgGΛlg → u64ΨΧY → ΤΠLΖCA → ΙΔjhOK → of1βme → αA6ΦΣ4 → ΦΟΗKD8 → ΝΒlfQG → wb5ΧqW → ΡQEΝΒC → ΕyaqTO → gVFΜwm → wR5ΧΑW → ΡZPΒsC → ΕcIΙpO → qgCΟlc → ΓE4ΨΞQ → ΤzbpSA → ΙXDΞuK → ΑoMΕdS → iYAΡtk → ΗL1βΗM → αljhg4 → Φ51βΨ8 → αΣΜFA4 → ΦΘvVK8 → ΝnPΒeG → wc8ΤpW → ΛQCΟΒI → ΓsaqZQ → cJFΜΙq → wpDΞcW → ΑQCΟΒS → ΓbXtqQ → cMEΝΖq → yjDΞiU → ΑU0γxS → γYSyt2 → αWKΗv4 → ΦmOΓf8 → Νe6ΦnG → Οw8ΤVE → ΛΑQΑRI → saYsra → KIGΛΚΙ → urndaY → MH9ΣΛΗ → ΙtjhYK → oL1βΗe → αl9Σg4 → ΦΙ4ΨJ8 → ΤΝocFA → ΙxBΠUK → ΕoSydO → gWAΡvm → ΗP5ΧΓM → ΡkcohC → ΕC2αΠO → ΨΔflO6 → Ρf5ΧmC → ΡΕ6ΦNC → ΟΕgkNE → Αh3ΩkS → ΦY2αt8 → ΨΝKΗF6 → ΡxlfUC → ΕT5ΧyO → ΡgUwlC → ΕS4ΨzO → ΤgWulA → ΙO4ΨΔK → ΤoemdA → ΙB7ΥΡK → ΝΖndMG → wj9ΣiW → ΙQ0γΒK → γoaqd2 → αGAΡΜ4 → ΦΗuWL8 → ΝlNΔgG → wg4ΨlW → ΤQ4ΨΒA → ΤΙaqJA → ΙpFΜcK → woCΟdW → ΓQAΡΒQ → ΗcaqpM → kGCΟΜi → Γv1βWQ → αcOΓp4 → ΦeCΟn8 → ΝΓ8ΤPG → ΛwcoVI → sRBΠΑa → ΕZHΚsO → sgIΙla → qI4ΨΚc → ΤrDΞaA → ΙΑGΛRK → uoYsdY → MKAΡΘΗ → ΗnjheM → k91βΤi → αΚ1βI4 → αΦqa74 → ΦΞFΜE8 → ΝzvVSG → wXPΒuW → cQMΕΒq → ibDΞqk → ΑF1βΝS → αxXtU4 → ΦTLΖy8 → ΝkUwhG → wS2αzW → ΨXPΒu6 → ΡcMΕpC → ΕiCΟjO → Γg0γlQ → γc4Ψp2 → αΤCΟ94 → ΦΚΒPI8 → ΝrbpaG → wHDΞΛW → ΑtPΒYS → cYKΗtq → mLDΞΗg → Αl5ΧgS → ΡY4ΨtC → ΤΕKΗNA → ΙmgkfK → o73ΩΦe → ΦΞ9ΣE8 → ΝΙySJG → wpVvcW → RPCΟΓΒ → ΓdZroQ → cIAΡΚq → ΗrDΞaM → ΑkGΛhS → uY2αtY → ΨMKΗΖ6 → ΡmiifC → Ε6δδΦO → ΧΔFΜO7 → ΟwemVE → ΑR7ΥΑS → ΝZXtsG → wMIΙΖW → qjPΒic → cE0γΞq → γzDΞS2 → αΑWuR4 → ΦZNΔs8 → ΝgIΙlG → wq4ΨbW → ΤQEΝΒA → ΙyaqTK → oVFΜwe → wR9ΣΑW → ΙZPΒsK → ocIΙpe → qD9ΣΟc → ΙΒDΞQK → ΑoaqdS → YGAΡΜu → ΗvLΖWM → ljOΓih → e40γΩo → γΥ9Σ82 → αΜΘJG4 → ΦvndW8 → ΝP9ΣΓG → ΙwcoVK → oRBΠΑe → ΕZ9ΣsO → ΙgIΙlK → qo4Ψdc → ΤEAΡΞA → ΙΗySLK → olVvge → QA4ΨΣΓ → ΤΘbpKA → ΙnDΞeK → Αo8ΤdS → ΛYAΡtI → ΗsKΗZM → mkIΙhg → q62αΧc → ΨΠDΞC6 → ΡΔzROC → ΕfXtmO → gM6ΦΖm → Οj5ΧiE → ΡΑ0γRC → γΕYsN2 → αhJΘk4 → Φo2αd8 → ΨΝAΡF6 → ΡΗwULC → ΕlRzgO → gY4Ψtm → ΤL5ΧΗA → ΡΙkgJC → Εp3ΩcO → ΦgCΟl8 → ΝΓ4ΨPG → ΤwcoVA → ΙRBΠΑK → ΕoYsdO → gKAΡΘm → Ηn5ΧeM → Ρk8ΤhC → ΛΕ2αNI → ΨsgkZ6 → ΡJ3ΩΙC → ΦΕocN8 → ΝhBΠkG → Εw2αVO → ΨgQΑl6 → Ρa4ΨrC → ΤΕGΛNA → ΙugkXK → oN3ΩΕe → Φh9Σk8 → ΝΙ2αJG → ΨwocV6 → ΡRBΠΑC → ΖΔYsON → ifJΘmk → o71βΦe → αΞ9ΣE4 → ΦΙySJ8 → ΝpVvcG → wQCΟΒW → ΓbPΒqQ → dbEΝqp → yFBΠΝU → ΕxTxUO → gUSyxm → WT5Χyw → ΡVPΒwC → ΕcQΑpO → gaCΟrm → ΓH5ΧΛQ → ΡtbpYC → ΕLDΞΗO → ΑlflgS → Y64ΨΧu → ΤΠLΖCA
743 max stepsT00000j → jSδδδyj → zihδjjT → yI0δγΚU → δΙeδmJ1 → γΙTδxJ2 → βΘeδmK3 → αΖSδyM4 → ΩΓcδoP5 → ΨyPδΒT6 → ΧxXδtU7 → ΦrPδΒa8 → ΥvQδΑW9 → ΤtTδxYA → ΣpOδΓcB → ΡtPδΒYC → ΠrSδyaD → ΟnNδΔeE → ΞrOδΓaF → ΝpRδzcG → ΜlMδΕgH → ΛpNδΔcI → ΚnQδΑeJ → ΙjLδΖiK → ΘnMδΕeL → ΗlPδΒgM → ΖhKδΗkN → ΘjNδΔiL → ΗkKδΗhM → ΘkOδΓhL → ΗjKδΗiM → ΘkNδΔhL → ΗkLδΖhM → ΗkNδΔhM → ΖjLδΖiN → ΗiMδΕjM → ΖkLδΖhN → ΗiNδΔjM → ΖjKδΗiN → ΘjMδΕiL → ΗlLδΖgM → ΗkOδΓhM → ΖiKδΗjN → ΘjMδΕiL