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 steps100
214 max steps20 → 1γ → α3Φ7ΝFwVaruXijγ1α3
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 → iδjiδj
419 max stepsB00Y → YAΡu → ΗLΖM → liih → 3δδα → α2α4 → ΨΥ76 → ΡΜFCΕvVOgPΒmc5ΧqΡDΞCΕzROgXtmM5ΧΗΡjhCΕ1βOαfl4Φ5Χ8ΡΜFC
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 → yTδxUyTδxU
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 → ΤΠLΖCAΙΔjhOKof1βmeαA6ΦΣ4ΦΟΗKD8ΝΒlfQGwb5ΧqWΡQEΝΒCΕyaqTOgVFΜwmwR5ΧΑWΡZPΒsCΕcIΙpOqgCΟlcΓE4ΨΞQΤzbpSAΙXDΞuKΑoMΕdSiYAΡtkΗL1βΗMαljhg4Φ51βΨ8αΣΜFA4ΦΘvVK8ΝnPΒeGwc8ΤpWΛQCΟΒIΓsaqZQcJFΜΙqwpDΞcWΑQCΟΒSΓbXtqQcMEΝΖqyjDΞiUΑU0γxSγYSyt2αWKΗv4ΦmOΓf8Νe6ΦnGΟw8ΤVEΛΑQΑRIsaYsraKIGΛΚΙurndaYMH9ΣΛΗΙtjhYKoL1βΗeαl9Σg4ΦΙ4ΨJ8ΤΝocFAΙxBΠUKΕoSydOgWAΡvmΗP5ΧΓMΡkcohCΕC2αΠOΨΔflO6Ρf5ΧmCΡΕ6ΦNCΟΕgkNEΑh3ΩkSΦY2αt8ΨΝKΗF6ΡxlfUCΕT5ΧyOΡgUwlCΕS4ΨzOΤgWulAΙO4ΨΔKΤoemdAΙB7ΥΡKΝΖndMGwj9ΣiWΙQ0γΒKγoaqd2αGAΡΜ4ΦΗuWL8ΝlNΔgGwg4ΨlWΤQ4ΨΒAΤΙaqJAΙpFΜcKwoCΟdWΓQAΡΒQΗcaqpMkGCΟΜiΓv1βWQαcOΓp4ΦeCΟn8ΝΓ8ΤPGΛwcoVIsRBΠΑaΕZHΚsOsgIΙlaqI4ΨΚcΤrDΞaAΙΑGΛRKuoYsdYMKAΡΘΗΗnjheMk91βΤiαΚ1βI4αΦqa74ΦΞFΜE8ΝzvVSGwXPΒuWcQMΕΒqibDΞqkΑF1βΝSαxXtU4ΦTLΖy8ΝkUwhGwS2αzWΨXPΒu6ΡcMΕpCΕiCΟjOΓg0γlQγc4Ψp2αΤCΟ94ΦΚΒPI8ΝrbpaGwHDΞΛWΑtPΒYScYKΗtqmLDΞΗgΑl5ΧgSΡY4ΨtCΤΕKΗNAΙmgkfKo73ΩΦeΦΞ9ΣE8ΝΙySJGwpVvcWRPCΟΓΒΓdZroQcIAΡΚqΗrDΞaMΑkGΛhSuY2αtYΨMKΗΖ6ΡmiifCΕ6δδΦOΧΔFΜO7ΟwemVEΑR7ΥΑSΝZXtsGwMIΙΖWqjPΒiccE0γΞqγzDΞS2αΑWuR4ΦZNΔs8ΝgIΙlGwq4ΨbWΤQEΝΒAΙyaqTKoVFΜwewR9ΣΑWΙZPΒsKocIΙpeqD9ΣΟcΙΒDΞQKΑoaqdSYGAΡΜuΗvLΖWMljOΓihe40γΩoγΥ9Σ82αΜΘJG4ΦvndW8ΝP9ΣΓGΙwcoVKoRBΠΑeΕZ9ΣsOΙgIΙlKqo4ΨdcΤEAΡΞAΙΗySLKolVvgeQA4ΨΣΓΤΘbpKAΙnDΞeKΑo8ΤdSΛYAΡtIΗsKΗZMmkIΙhgq62αΧcΨΠDΞC6ΡΔzROCΕfXtmOgM6ΦΖmΟj5ΧiEΡΑ0γRCγΕYsN2αhJΘk4Φo2αd8ΨΝAΡF6ΡΗwULCΕlRzgOgY4ΨtmΤL5ΧΗAΡΙkgJCΕp3ΩcOΦgCΟl8ΝΓ4ΨPGΤwcoVAΙRBΠΑKΕoYsdOgKAΡΘmΗn5ΧeMΡk8ΤhCΛΕ2αNIΨsgkZ6ΡJ3ΩΙCΦΕocN8ΝhBΠkGΕw2αVOΨgQΑl6Ρa4ΨrCΤΕGΛNAΙugkXKoN3ΩΕeΦh9Σk8ΝΙ2αJGΨwocV6ΡRBΠΑCΖΔYsONifJΘmko71βΦeαΞ9ΣE4ΦΙySJ8ΝpVvcGwQCΟΒWΓbPΒqQdbEΝqpyFBΠΝUΕxTxUOgUSyxmWT5ΧywΡVPΒwCΕcQΑpOgaCΟrmΓH5ΧΛQΡtbpYCΕLDΞΗOΑlflgSY64ΨΧuΤΠLΖCA
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 → ΘjMδΕiLΗlLδΖgMΗkOδΓhMΖiKδΗjNΘjMδΕiL