Base 112: Maximum Iteration Sequences: Full Cycle

Blog: The First Pixel: Kaprekar's Constant 6174

Radix Character Encoding
0123456789ABCDEF
GHIJKLMNOPQRSTUV
WXYZabcdefghijkl
mnopqrstuvwxyzΑΒ
ΓΔΕΖΗΘΙΚΛΜΝΞΟΠΡΣ
ΤΥΦΧΨΩαβγδεζηθικ
λμνξοπρςστυφχψωА

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
216 max steps20 → 1ω → χ3 → σ7 → λF → ΤV → mΒ → Eμ → ΦT → qx → 6τ → νD → ΨR → ut → 0А → ω1 → χ3
358 max steps100 → 0АА → ωА1 → ψА2 → χА3 → φА4 → υА5 → τА6 → σА7 → ςА8 → ρА9 → πАA → οАB → ξАC → νАD → μАE → λАF → κАG → ιАH → θАI → ηАJ → ζАK → εАL → δАM → γАN → βАO → αАP → ΩАQ → ΨАR → ΧАS → ΦАT → ΥАU → ΤАV → ΣАW → ΡАX → ΠАY → ΟАZ → ΞАa → ΝАb → ΜАc → ΛАd → ΚАe → ΙАf → ΘАg → ΗАh → ΖАi → ΕАj → ΔАk → ΓАl → ΒАm → ΑАn → zАo → yАp → xАq → wАr → vАs → uАt → tАu → tАu
424 max steps2005 → 51ψφ → χπ94 → σζJ8 → λΚdG → ΤVΣW → nkΓΒ → IDμι → ΨΞZS → udΚu → VААΤ → ΤUΤW → olΒΑ → GBξλ → γΣVO → ΓlΒm → HEλκ → ΦΠXU → qhΖy → O7ςγ → λΒlG → ΤFκW → ΤlΒW → mFκΓ → ΤFκW
547 max steps10009 → 90Аως → АοАA1 → ωοАA2 → ψξАB3 → χμАD4 → φιАG5 → υεАK6 → τΩАP7 → σΣАV8 → ςΛАc9 → ρΓАkA → πtАtB → οjАΔC → ξsАuD → νiАΕE → μrАvF → λhАΖG → κqАwH → ιgАΗI → θpАxJ → ηfАΘK → ζoАyL → εeАΙM → δnАzN → γdАΚO → βmАΑP → αcАΛQ → ΩlАΒR → ΨbАΜS → ΧkАΓT → ΦaАΝU → ΥjАΔV → ΤZАΞW → ΣiАΕX → ΡYАΟY → ΠhАΖZ → ΟXАΠa → ΡeАΙY → ΠbАΜZ → ΟdАΚa → ΞaАΝb → ΞbАΜb → ΝbАΜc → ΝZАΞc → ΟaАΝa → ΞdАΚb → ΝZАΞc
6385 max steps3000An → nA2χπΒ → υζDμK6 → οΨΙeRC → γvTΥsO → Γq2χxm → υG6σκ6 → ονΡWDC → γΩjΔQO → ΓxJζqm → ΛG6σκe → νΣVΣWE → ΨmkΓΒS → uIEλθu → ΦΝААaU → ΥΞ7ςaV → λocΛzG → ΤYAοΠW → εmgΗΒM → ΗQEλΩi → ΦxNβqU → Γq6σxm → νG6σκE → νΨΡWRE → ΨvjΔsS → uK2χζu → υΙААe6 → τΚZΞe7 → νeUΤΚE → ΨoUΤzS → uoAοzu → εAААοM → πδ9πMB → ηεΕiLK → ΛΘLδge → ΗWQΨΣi → wlNβΓs → ΓH3φιm → σΠFκY8 → λΤgΗVG → ΤnPΩΑW → ymCνΒq → αF7ςλQ → λΥxpUG → Τp7ςyW → λm8ρΒG → ιΤEλVI → ΦΟmΑZU → qfDμΙy → ΨT7ςΦS → λuqwtG → Τ60ωτW → ωξlΒC2 → χβFκO4 → σΤΑmV8 → λnDμΑG → ΨΤCνVS → αumΑtQ → yE0ωμq → ωΧ7ςS2 → χλsuF4 → σΥ1ψU8 → χλoyF4 → σΥ9πU8 → ληoyJG → ΤΜ9πcW → ηmYΟΒK → ΛgEλΘe → ΦWQΨΣU → wqkΓxs → I73φσι → σμΞZE8 → λΧdΚSG → ΤtVΣuW → nl0ωΓΒ → ωHDμι2 → χΨΟYR4 → σvfΘs8 → λS2χΧG → υΤsuV6 → οn1ψΑC → χγCνN4 → σαΓkP8 → λzHθoG → ΤΟAοZW → εmeΙΒM → ΗUEλΥi → ΦpNβyU → Γq8ρxm → ιG6σκI → νΣΞZWE → ΨldΚΓS → uWGιΣu → ΡkААΓY → ΠΔDμkZ → ΨgIηΘS → ΝuQΨtc → wa0ωΞs → ωd3φΛ2 → χσWΡ74 → σμjΔE8 → λΧJζSG → ΤΛsudW → mX1ψΡΓ → χjFκΕ4 → σΤKεV8 → λΙmΑfG → ΤTDμΦW → ΨrlΒwS → uG4υκu → ρΡААWA → πΣNβWB → εΓkΓlM → ΗIGιθi → ΡΞNβaY → ΓicΛΖm → YNFκγΡ → ΤΔhΖkW → mOIηβΓ → ΝΒFκmc → ΤaEλΞW → ΦmcΛΒU → qYEλΠy → Φh7ςΗU → λqOαxG → ΤΑ6σnW → νmCνΒE → αΨEλRQ → ΦyuspU → q91ψρy → χθ7ςI4 → σλΝaF8 → λΥbΜUG → ΤpZΞyW → me8ρΚΓ → ιVFκΤI → ΤΟmΑZW → mfDμΙΓ → ΨTFκΦS → ΤuqwtW → m60ωτΓ → ωξFκC2 → χβΣVO4 → σΒlΒm8 → λGEλκG → ΦΤΡWVU → qnjΔΑy → KD7ςνη → λΩΚdQG → ΤxVΣqW → nl6σΓΒ → νHDμιE → ΩΧΟYSR → wtfΘus → S40ωφΨ → ωςtt82 → χιААG4 → φκDμG5 → ρΨΡWRA → ηvjΔsK → ΛK2χζe → υΚVΣe6 → οmUΤΒC → γoEλzO → ΦΓAοlU → εqGιxM → ΡΗ6σhY → νiOαΖE → ΨΑMγnS → ΕuCνtk → αK0ωζQ → ωΚxpe2 → χV7ςΤ4 → σλmΑF8 → λΥDμUG → ΨΤoyVS → un9πΑu → ηCААνK → ξζ5τKD → οαΙePC → γzTΥoO → ΓqAοxm → εG6σκM → νΣΖhWE → ΨlNβΓS → ΓuGιtm → ΡG0ωκY → ωΣhΖW2 → χlNβΓ4 → σΓGιl8 → λΡGιXG → ΤΡiΕXW → mjLδΕΓ → ΗLFκεi → ΤΘNβgW → ΓmQΨΒm → wGEλκs → ΦΣ3φWU → σqkΓx8 → λI6σθG → νΤΝaVE → ΨnbΜΑS → uaCνΞu → αcААΛQ → ΩΜDμcR → ΨwYΟrS → ug4υΘu → ρQААΨA → πΩHθQB → εΟwqZM → Ηf5τΙi → οTNβΦC → γΓqwlO → ΓH5τιm → οΠFκYC → γΤgΗVO → ΓnPΩΑm → yGCνκq → αΣ7ςWQ → λykΓpG → ΤI8ρθW → ιΞlΒaI → ΟdFκΛa → ΤeWΡΚW → mkUΤΔΓ → oJFκηΑ → ΤΜBξcW → γmYΟΒO → ΓgEλΘm → ΦRFκΨU → ΤvpxsW → m82χςΓ → υκFκG6 → οΤΡWVC → γnjΔΑO → ΓKCνζm → αΚFκeQ → ΤyUΤpW → om8ρΒΑ → ιFBξλI → γΥΞZUO → ΓpdΚym → WG8ρκΤ → ιΣlΒWI → ΟlFκΓa → ΤeGιΚW → ΡmUΤΒY → oiEλΖΑ → ΦNBξγU → γΔpxkO → ΓJ7ςηm → λΜFκcG → ΥΣYΟWV → olfΘΓΑ → SHBξιΨ → γΠttYO → ΓgААΗm → ΘΒ3φmh → σQEλΩ8 → λΦwqTG → Τr5τwW → οm4υΒC → ργEλNA → ηΦΓkTK → ΛrHθwe → ΟW4υΣa → ρldΚΓA → ηWGιΣK → ΡΛkΓdY → iXHθΡΗ → ΟjNβΕa → ΓeKεΚm → ΙVFκΤg → ΤnRΧΑW → umCνΒu → αEААλQ → μΩ9πQF → ηΦwqTK → Λr5τwe → οW4υΣC → ργkΓNA → ηΔHθkK → ΟΛIηda → ΝeWΡΚc → kaUΤΞΕ → odJζΛΑ → ΛXBξΡe → γjVΣΕO → ΓmKεΒm → ΙGEλκg → ΦΣRΧWU → uqkΓxu → I6ААσι → τθ9πI7 → νηΝaJE → ΨΜbΜcS → uaYΟΞu → gcААΛΙ → ΜΘ1ψgd → χYQΨΠ4 → σwgΗr8 → λQ4υΩG → ρΤwqVA → ηn5τΑK → οΛCνdC → γαWΡPO → ΓzjΔom → KGAοκη → εΣΚdWM → ΗlVΣΓi → mOGιβΓ → ΡΒFκmY → ΤiEλΖW → ΦmMγΒU → ΕqEλxk → ΦK6σζU → νΚpxeE → ΨV7ςΤS → λumΑtG → ΤE0ωμW → ωΧlΒS2 → χtFκu4 → σΤ0ωV8 → ωλmΑF2 → χΥDμU4 → σΨoyR8 → λv9πsG → ηΤ2χVK → υΛmΑd6 → οXDμΡC → γΨiΕRO → ΓvLδsm → ΗG2χκi → υΣNβW6 → οΓkΓlC → γIGιθO → ΡΞΒlaY → idFκΛΗ → ΤXNβΡW → ΓmiΕΒm → MGEλκε → ΦΣΖhWU → qlNβΓy → ΓH7ςιm → λΠFκYG → ΥΣgΗWV → olPΩΓΑ → yHBξιq → γΠ7ςYO → λΓgΗlG → ΤQGιΩW → ΡxlΒqY → iG6σκΗ → νΣNβWE → ΨΓkΓlS → uIGιθu → ΡΝААaY → ΠΞ3φaZ → σgcΛΘ8 → λYQΨΠG → ΤwgΗrW → mQ4υΩΓ → ρxFκqA → ηΤ6σVK → νΛmΑdE → ΨXDμΡS → ΨuiΕtS → uM0ωδu → ωΕААi2 → ψΖhΖi3 → υOMγβ6 → οΕΑmjC → γLDμεO → ΨΘΒlgS → uRFκΨu → ΤuААsW → ΣvNβsX → Γk2χΔm → υJFκη6 → οΤΛcVC → γnXΠΑO → ΓiCνΖm → αNFκγQ → ΤΔxpkW → mJ7ςηΓ → λΜFκcG