Base 104: Maximum Iteration Sequences: Cycle Start

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
Cycle Start
11 max steps10
22 max steps20 → 1ρ → ο3
353 max steps100 → 0ςς → ρς1 → πς2 → ος3 → ξς4 → νς5 → μς6 → λς7 → κς8 → ις9 → θςA → ηςB → ζςC → εςD → δςE → γςF → βςG → αςH → ΩςI → ΨςJ → ΧςK → ΦςL → ΥςM → ΤςN → ΣςO → ΡςP → ΠςQ → ΟςR → ΞςS → ΝςT → ΜςU → ΛςV → ΚςW → ΙςX → ΘςY → ΗςZ → Ζςa → Εςb → Δςc → Γςd → Βςe → Αςf → zςg → yςh → xςi → wςj → vςk → uςl → tςm → sςn → rςo → qςp → pςq
413 max steps4009 → 93ξκ → λΩH8 → γΖZG → ΛVΚW → fcΓΒ → QLΥΡ → yppi → Fςςγ → γEγG → ΝΚVU → idΒy → OFβΤ → ΛtlW
541 max stepsp0000 → oςςςr → rnςrp → s1ςπo → ρoςq2 → πpςp3 → οnςr4 → ξoςq5 → νmςs6 → μnςr7 → λlςt8 → κmςs9 → ιkςuA → θlςtB → ηjςvC → ζkςuD → εiςwE → δjςvF → γhςxG → βiςwH → αgςyI → ΩhςxJ → ΨfςzK → ΧgςyL → ΦeςΑM → ΥfςzN → ΤdςΒO → ΣeςΑP → ΡcςΓQ → ΠdςΒR → ΟbςΔS → ΞcςΓT → ΝaςΕU → ΜbςΔV → ΛZςΖW → ΚaςΕX → ΙYςΗY → ΘZςΖZ → ΗXςΘa → ΙWςΙY → ΚZςΖX → ΙZςΖY
6221 max stepsB000XΞ → ΞXAηΙT → ΦkaΕvM → yUAηΜi → ΦhFβyM → ΛyGαhW → ΙeGαΒY → ΙaMΤΖY → waUΛΖk → gVBζΛΑ → ΤfJΧΑO → ΓuKΦle → ΑO8ιΣg → αtJΧmI → ΗΓ6λda → εWOΡΚE → ΟscΓnS → mQ4νΠu → ιp7κqA → γΨ0ρJG → ρΛΓcV2 → οfPΠΑ4 → λqKΦp8 → γΑ0ρfG → ρΛKΦV2 → οΑeΑf4 → λMKΦΥ8 → γΑwifG → ΛLDδΦW → ΟzdΒgS → mOIΨΣu → Εt7κmc → γS6λΞG → εΛkuVE → Οf9θΑS → ΨmKΦtK → ΓΑ6λfe → εOKΦΣE → ΟΑsmfS → mL5μΦu → ηz7κgC → γΤIΨNG → ΛΕukbW → eT9θΝΓ → ΨjNΣwK → ΓuCεle → ΡO8ιΣQ → αtppmI → Η6ςςλa → μΖRΞa7 → εmUΛtE → Οg6λzS → εmIΨtE → ΟΕ6λbS → εmSΝtE → Οk6λvS → εmAηtE → ΦΟ6λRM → εymshE → ΟH5μαS → ηΘltYC → ΤZ7κΗO → γuWΙlG → Λc8ιΔW → αeQΟΒI → ΗoMΤra → wW2οΚk → νdBζΓ6 → ηΤOΡNC → ΤvrnkO → uB3ξηm → λΥ7κM8 → δβwiGF → ΝΚDδWU → ΟicΓxS → mQEγΠu → Νp7κqU → γi0ρxG → ρΛEγV2 → οΝeΑT4 → λjLΥw8 → γyCεhG → ΡΛGαVQ → ΙqeΑpY → aM0ρΥΗ → ρxVΚi2 → οeEγΒ4 → λΝMΤT8 → γwiwjG → ΛECεδW → ΡΞdΒSQ → qlNΣuq → u8ςςιm → κtbΔm9 → αS6λΞI → εΗkuZE → ΟX9θΙS → ΨmaΕtK → ΓU6λΜe → εhNΣyE → ΟuGαlS → Ιm8ιtY → αa6λΖI → εΗUΛZE → ΟgWΙzS → mcIΨΔu → ΕR7κΟc → γnRΞsG → Λm4νtW → ιe6λΒA → εΨMΤJE → ΟΔvjcS → mRBζΟu → Τn7κsO → γu4νlG → ιΛ8ιVA → αΨeΑJI → ΗΔLΥca → yWQΟΚi → odFβΓs → ΛP3ξΡW → λrdΒo8 → γO2οΣG → νΛsmV6 → ηf5μΑC → ηΤKΦNC → ΤΑukfO → uL9θΦm → Ψz7κgK → γΓIΨdG → ΛΕOΡbW → seSΝΒo → kN3ξΤw → λvBζk8 → γΤAηNG → ΦΛukVM → yf9θΑi → ΨLFβΦK → ΛΓygdW → ePHΩΡΓ → ΗrNΣoa → uW2οΚm → νd7κΓ6 → ηγOΡFC → ΤΜrnUO → uh3ξym → λH7κα8 → δβΗYGF → ΝΚXΘWU → idZΖΓy → WPFβΡΛ → ΛrdΒoW → eO2οΣΓ → νtNΣm6 → ηu6λlC → εΤ8ιNE → αΟukRI → Ηn9θsa → ΨW4νΚK → ιΓcΓdA → ΨQOΡΠK → Γsoqne → O51πνΤ → οθtlA4 → λΧ7κK8 → δβΑeGF → ΝΚLΥWU → yicΓxi → QGEγβΡ → ΝΚppWU → icςςΓy → Δx3ξid → λQEγΠ8 → γΝoqTG → Λj1πwW → οeCεΒ4 → λΡMΤP8 → γwqojG → ΛD1πεW → οΠdΒQ4 → λpNΣq8 → γu0ρlG → ρΛ8ιV2 → οαeΑH4 → λΘLΥY8 → γyYΗhG → ΛYGαΘW → ΙeYΗΒY → aYMΤΘΗ → wZVΚΗk → eXBζΙΓ → ΤbNΣΕO → vtSΝml → kA6λθw → εΧBζKE → ΤΟΑeRO → unLΥsm → y84νκi → ιβFβGA → ΨΛΙWVK → ΓfbΔΑe → SOKΦΣΟ → Αtltmg → K86λκΨ → εβΒdGE → ΟΚNΣWS → umcΓtm → Q86λκΡ → εβppGE → ΟΙςςWS → ΞΚ5μWT → ηkcΓvC → ΤQAηΠO → ΦuoqlM → y91πιi → οΩFβI4 → λΛΕaV8 → γfTΜΑG → ΛiKΦxW → ΑeEγΒg → ΝNJΧΤU → Γvhxke