Base 114: Maximum Iteration Sequences: Full Cycle

Blog: The First Pixel: Kaprekar's Constant 6174

Radix Character Encoding
0123456789ABCDEF
GHIJKLMNOPQRSTUV
WXYZabcdefghijkl
mnopqrstuvwxyzΑΒ
ΓΔΕΖΗΘΙΚΛΜΝΞΟΠΡΣ
ΤΥΦΧΨΩαβγδεζηθικ
λμνξοπρςστυφχψωА
БВГДЕЖЗИЙКЛМНОПР

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
246 max steps20 → 1Б → ω3υ7νFΦVγPΑpηLΙhyrοDαRwtχ5ρBεNΕlΟbΤXΛfqzλHΡZuvБ1ω3
359 max steps100 → 0ВВ → БВ1 → АВ2 → ωВ3 → ψВ4 → χВ5 → φВ6 → υВ7 → τВ8 → σВ9 → ςВA → ρВB → πВC → οВD → ξВE → νВF → μВG → λВH → κВI → ιВJ → θВK → ηВL → ζВM → εВN → δВO → γВP → βВQ → αВR → ΩВS → ΨВT → ΧВU → ΦВV → ΥВW → ΤВX → ΣВY → ΡВZ → ΠВa → ΟВb → ΞВc → ΝВd → ΜВe → ΛВf → ΚВg → ΙВh → ΘВi → ΗВj → ΖВk → ΕВl → ΔВm → ΓВn → ΒВo → ΑВp → zВq → yВr → xВs → wВt → vВu → uВvuВv
416 max stepsE00h → hDξΚ → αRΩS → xuut → 3ВВω → ω2ω4 → χτ76 → ρμFCεΥVOΕnΒmIDξλαΠZSwfΚuU1АΨωrx4υ5φ8ρμFC
549 max steps10000 → 0ВВВВ → БВВВ1 → Б0ВБ2 → ВψВ31 → БψВ32 → АχВ43 → ωυВ64 → ψςВ95 → χξВD6 → φιВI7 → υγВO8 → τΥВV9 → σΜВdA → ςΓВmB → ρsВwC → πlВΔD → οrВxE → ξkВΕF → νqВyG → μjВΖH → λpВzI → κiВΗJ → ιoВΑK → θhВΘL → ηnВΒM → ζgВΙN → εmВΓO → δfВΚP → γlВΔQ → βeВΛR → αkВΕS → ΩdВΜT → ΨjВΖU → ΧcВΝV → ΦiВΗW → ΥbВΞX → ΤhВΘY → ΣaВΟZ → ΡgВΙa → ΠZВΠb → ΡdВΜa → ΠcВΝb → ΟcВΝc → ΞbВΞd → ΟZВΠc → ΡcВΝa → ΠdВΜb → ΟbВΞcΟbВΞc
6764 max steps2000ВВ → ВВ1А01 → ВБψ311 → БАτ722 → ωψμF44 → υτΥV88 → νμnΒGG → ΦΥDξWW → αomΓΒS → wGCομu → γΥ1АWQ → ωΑmΓp4 → υGAρμ8 → νηΤWLG → ΦΚlΔgW → oTHκΨΓ → ΡtDξwa → αg2ωΚS → χwSΨt6 → ρu2ωvC → χε0БN6 → БρΕkB2 → ωζJθM4 → υΝΗid8 → νZNδΡG → ΦΕgΙlW → oSIιΩΓ → ΟvDξuc → αc0БΞS → БwaΟt2 → ωe2ωΜ4 → χυWΤ76 → ρξlΔEC → εΩHκSO → ΡΕuula → gIВВιΛ → κΚLζgJ → ΟΙSΨhc → ucQαΞw → yb1АΟs → ωd5φΝ4 → υρYΡB8 → νζhΘMG → ΦΘPβiW → ΑoOγΒq → ΓD9ςοo → ιβDξQK → αΝyqdS → wZ7τΡu → νh1АΙG → ωΦQαV4 → υyoΑr8 → νC6υπG → οδΥVOE → αΔnΒmS → wHDξλu → αΣ1АYS → ωwiΗt4 → υO2ωδ8 → χνΓmF6 → ρΧFμUC → εΦqyVO → Εp7τΑm → νIAρκG → ηΦΟaVM → ΙpdΜΑi → YQAρβΤ → ηzjΖqM → ΙM8σζi → λΘPβiI → ΡΑOγpa → ΓgAρΚo → ηTDξΨM → αΙswhS → wR3ψαu → υx1Аs8 → ων4χF4 → υσΦU98 → νκpzIG → ΦΠ9ςaW → ιoeΛΒK → ΝWCοΥe → γnXΣΓQ → ΑkEνΖq → ΨL9ςηU → ιΚrxgK → ΝT5φΨe → ρtXΣwC → εk2ωΖO → χΕKηl6 → ρΛIιfC → εΟUΦbO → ΕqcΝzm → aI8σκΡ → λΠfΚaI → ΡfTΧΛa → sgUΦΚy → qT5φΨΑ → ρt9ςwC → ιε2ωNK → χΝΕkd6 → ρZJθΡC → εΝgΙdO → ΕZRΩΡm → whHκΙu → ΡR1Аαa → ωxfΚs4 → υU4χΧ8 → σνqyFA → ιΧ7τUK → νΝqydG → ΦZ7τΡW → νogΙΒG → ΦSCοΩW → γvnΒuQ → ΑE0Бξq → БΩ9ςS2 → ωιuuJ4 → υΝВВc8 → τΞVΥc9 → λoaΟΒI → ΡeCοΜa → γgWΤΚQ → ΑmSΨΔq → uH9ςλw → ιΣ1АYK → ωΝiΗd4 → υZNδΡ8 → νΕgΙlG → ΦSIιΩW → ΟvnΒuc → cE0БξΟ → БΩbΞS2 → ωvbΞu4 → υc0БΞ8 → БνaΟF2 → ωΧdΜU4 → υrXΣy8 → νk6υΖG → οΦKηVE → αΛoΑfS → wVBπΦu → εp1АΑO → ωΕAρl4 → υηIιL8 → νΟΙgbG → ΦdRΩΝW → woYΡΒu → iD1АοΙ → ωβPβQ4 → υΑyqp8 → νB7τρG → νζΥVMG → ΦΘnΒiW → oPDξγΓ → αΒDξoS → αwCοtS → γw2ωtQ → χΑ2ωp6 → χρAρB6 → ρηεMLC → εΚΖjgO → ΕTLζΨm → ΙtHκwi → ΡQ2ωβa → χzfΚq6 → ρU8σΧC → λεqyNI → ΡΖ7τka → νgKηΚG → ΦΛSΨfW → uoUΦΒw → qD1АοΑ → ωβ9ςQ4 → υιyqJ8 → νΞ7τcG → νΦaΟVG → ΦpdΜΑW → oYAρΣΓ → ηjDξΗM → αΙMεhS → ΗwQαtk → yM2ωζs → χΘ5φi6 → ςπOγCB → ηδΒnOM → ΙΔDξmi → αQGλβS → ΤzvtqY → k91АσΗ → ωκLζI4 → υΠΘha8 → νfPβΛG → ΦΑUΦpW → qoAρΒΑ → ηD9ςοM → ιβΘhQK → ΝzPβqe → ΑY8σΣq → λj9ςΗI → ιΡMεZK → ΝΗgΙje → YSMεΩΤ → ΗvjΖuk → NL0Бηζ → БΚΖjg2 → ωTLζΨ4 → υΙswh8 → νR3ψαG → υΦwsV8 → νp3ψΑG → υΦAρV8 → νηoΑLG → ΦΚBπgW → εoSΨΒO → ΕuCοvm → γI0БκQ → БΠzpa2 → ωf9ςΛ4 → υιUΦJ8 → νΞpzcG → Φb9ςΟW → ιocΝΒK → ΝaCοΠe → γfXΣΛQ → ΑkUΦΖq → qL9ςηΑ → ιΚ9ςgK → ιΝSΨdK → ΝuYΡve → iY0БΣΙ → БjPβΗ2 → ωΑMεp4 → υΗAρj8 → νηMεLG → ΦΚΖjgW → oTLζΨΓ → ΙtDξwi → αQ2ωβS → χzvtq6 → ρ91АσC → ωκδNI4 → υΠΔla8 → νfHκΛG → ΦΡUΦZW → qogΙΒΑ → SD9ςοα → ιβvtQK → Νz1Аqe → ωY8σΣ4 → υλiΗH8 → νΣNδYG → ΦΕiΗlW → oOIιδΓ → ΟΔDξmc → αcGλΞS → ΤwaΟtY → ke2ωΜΗ → χXLζΤ6 → ρΙkΕhC → εRJθαO → ΝΕwsle → YJ3ψιΤ → υΞjΖc8 → νbLζΟG → ΦΙcΝhW → oaQαΠΓ → yfDξΛs → αV5φΦS → ρwoΑtC → εC2ωπO → χδΔlO6 → ρΔHκmC → εΡGλZO → ΤΕgΙlY → kSIιΩΗ → ΟvLζuc → Ιc0БΞi → БbPβΟ2 → ωΑcΝp4 → υaAρΠ8 → νηeΛLG → ΦΚVΥgW → pnSΨΓΒ → uFBπνw → εΧ1АUO → ωΕqyl4 → υJ7τι8 → ξμΝcGF → ΨΥZΠWU → snfΚΓy → UF5φνΨ → ρΧrxUC → εr5φyO → ρΕ6υlC → οεIιNE → αΟΕkbS → wdJθΝu → ΝZ1АΡe → ωhXΣΙ4 → υkQαΖ8 → νyKηrG → ΦΛ6υfW → οoUΦΒE → αqCοzS → γw8σtQ → λΑ2ωpI → χΡAρZ6 → ρηgΙLC → εΚRΩgO → ΕwSΨtm → uI2ωκw → χΠ1Аa6 → ωρeΛB4 → υζVΥM8 → νΘnΒiG → ΦPDξγW → αΒnΒoS → wECοξu → γΩ1АSQ → ωΑuup4 → υAВВρ8 → τς3ψA9 → υληKH8 → νΣΚfYG → ΦjTΧΗW → soMεΒy → ΗD5φοk → ρβLζQC → εΙyqhO → ΕR7ταm → νxHκsG → ΦΡ4χZW → σogΙΒA → ιSCοΩK → γΝuudQ → ΑYВВΡq → ΣzFμqZ → Φi8σΘW → λoOγΒI → ΡΓCοna → γgEνΚQ → ΨΑSΨpU → usAρxw → η51АχM → ωςΘhA4 → υθPβK8 → νΜzpeG → ΦX9ςΤW → ιokΕΒK → ΝKCοθe → γΜXΣeQ → ΑkWΤΖq → mL9ςηΕ → ιΚHκgK → ΡΝSΨda → ugYΡΚw → iT1АΨΙ → ωtPβw4 → υΑ2ωp8 → χνAρF6 → ρηΦULC → εΚpzgO → ΕT9ςΨm → ιtHκwK → ΡΝ2ωda → χgYΡΚ6 → ρiSΨΘC → εuOγvO → ΕΓ0Бnm → БIEνκ2 → ωΨΟaT4 → υtdΜw8 → νY2ωΣG → χΦiΗV6 → ρpNδΑC → εΕAρlO → ηΕIιlM → ΟΙIιhc → ΟcQαΞc → ycaΟΞs → eb5φΟΝ → ρdXΣΝC → εkYΡΖO → ΕiKηΘm → ΛPHκγg → ΡΒTΧoa → sgCοΚy → γT5φΨQ → ρΑswpC → εB3ψρO → υζΔlM8 → νΘHκiG → ΦΡOγZW → ΓogΙΒo → SECοξα → γΩvtSQ → Αv1Аuq → ωA0Бς4 → БυηK72 → ωξΚfE4 → υΩTΧS8 → νvrxuG → Φ60БφW → БπnΒC2 → ωδDξO4 → υαΓmR8 → νxFμsG → ΧΥ4χWV → σqmΓzA → ιG8σμK → λΥΜdWI → ΡnXΣΓa → kgEνΚΗ → ΨTLζΨU → Ιtrxwi → Q62ωφγ → χπzpC6 → ρδ9ςOC → ιεΓmNK → ΝΖFμke → ΦYKηΣW → ΛoiΗΒg → UOCοδΨ → γΔrxmQ → ΑH5φλq → ρΣ9ςYC → ιεiΗNK → ΝΖNδke → ΕYKηΣm → ΛjHκΗg → ΡUMεΧa → ΗrfΚyk → UM6υζΨ → οΘrxiE → αP5φγS → ρΒvtoC → εD1АοO → ωβΔlQ4 → υzHκq8 → νΡ8σZG → λΦgΙVI → ΡpRΩΑa → wgAρΚu → ηT1АΨM → ωΙswh4 → υR3ψα8 → υνwsF8 → νΧ3ψUG → υΦqyV8 → νp7τΑG → νΦAρVG → ηΦoΑVM → ΙpBπΑi → εQAρβO → ηΕyqlM → ΙJ7τιi → νΞPβcG → ΦΑaΟpW → oeAρΜΓ → ηXDξΤM → αΙkΕhS → wRJθαu → Νx1Аse → ωY4χΣ4 → υσiΗ98 → νκNδIG → ΦΠΔlaW → ofHκΛΓ → ΡVDξΦa → αpfΚΑS → wUAρΧu → ηr1АyM → ωΙ6υh4 → υοQαD8 → νβxrQG → Φz5φqW → ρo8σΒC → λεCοNI → γΡΕkZQ → ΑhJθΙq → ΝR9ςαe → ιxXΣsK → Νk4χΖe → σYKηΣA → ιΛiΗfK → ΝVNδΦe → ΕpXΣΑm → kIAρκΗ → ηΠLζaM → ΚΘeΛih → WSOγΩΦ → ΓvnΒuo → FD0Бοξ → БβΧTQ2 → ωzrxq4 → υ95φσ8 → ρνιIFC → εΧΞbUO → ΕrbΞym → cI6υκΟ → οΠbΞaE → αfbΞΛS → wcUΦΞu → qb1АΟΑ → ωd9ςΝ4 → υιYΡJ8 → νΞhΘcG → ΦbPβΟW → ΑocΝΒq → aD9ςοΡ → ιβfΚQK → ΝzTΧqe → sY8σΣy → λj5φΗI → ρΡMεZC → εΗgΙjO → ΕSMεΩm → ΗvHκuk → ΡM0Бζa → БΘfΚi2 → ωUOγΧ4 → υΓqyn8 → νF7τνG → νΧΥVUG → ΦrnΒyW → oE6υξΓ → οΩDξSE → βΩuuSR → yuВВus → xv3ψut → υ40Бψ8 → БτμF82 → ωμΥVG4 → υΥnΒW8 → νnDξΓG → αΦEνVS → ΨwoΑtU → sC2ωπy → χδ5φO6 → ςπΓmCB → ηδFμOM → ΦΙΓmhW → oRFμαΓ → ΦxDξsW → αo4χΒS → σwCοtA → ιγ2ωPK → χΝΑod6 → ρZBπΡC → ζδgΙON → ΗΔRΩmk → wMGλζu → ΤΘ1АiY → ωkOγΖ4 → υΓKηn8 → νΛEνfG → ΨΦUΦVU → sqoΑzy → C95φσρ → ρκδNIC → εΠΔlaO → ΕfHκΛm → ΡVHκΦa → ΡpfΚΑa → gUAρΧΛ → ηrTΧyM → Ιs6υxi → οQ4χβE → σαyqRA → ιx7τsK → νΝ4χdG → σΦYΡVA → ιphΘΑK → ΝQAρβe → ηzXΣqM → Ιk8σΖi → λQKηβI → ΡΛyqfa → gV7τΦΛ → νpTΧΑG → ΦsAρxW → ηo4χΒM → σΙCοhA → ιγQαPK → ΝΒxroe → YD5φοΤ → ρβjΖQC → εzLζqO → ΙΕ8σli → λQIιβI → ΡΟyqba → gd7τΝΛ → νZTΧΡG → ΦsgΙxW → oS4χΩΓ → σvDξuA → ια0БRK → БΝwsd2 → ωZ3ψΡ4 → φτgΙ87 → ομRΩGE → αΥvtWS → wn1АΓu → ωF1Аν4 → ωυΦU74 → υξpzE8 → νΩ9ςSG → ιΦuuVK → ΝoВВΑe → ΜΒBπof → εWCοΥO → γΕmΓlQ → ΑJFμιq → ΦΞ9ςcW → ιoaΟΒK → ΝeCοΜe → γYWΤΣQ → ΑmiΗΔq → OH9ςλε → ιΣΔlYK → ΝjHκΗe → ΡYMεΣa → ΗjfΚΗk → UNLζεΨ → ΙΖrxki → QL5φηγ → ρΚzpgC → εT9ςΨO → ιΕswlK → ΝJ3ψιe → υΞXΣc8 → νkaΟΖG → ΦeKηΜW → ΛoWΤΒg → mUCοΧΕ → γrHκyQ → 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