Base 113: Maximum Iteration Sequences: Cycle Start

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
Cycle Start
11 max steps10
23 max steps10 → 0Б → А1 → ψ3
357 max steps100 → 0ББ → АБ1 → ωБ2 → ψБ3 → χБ4 → φБ5 → υБ6 → τБ7 → σБ8 → ςБ9 → ρБA → πБB → οБC → ξБD → νБE → μБF → λБG → κБH → ιБI → θБJ → ηБK → ζБL → εБM → δБN → γБO → βБP → αБQ → ΩБR → ΨБS → ΧБT → ΦБU → ΥБV → ΤБW → ΣБX → ΡБY → ΠБZ → ΟБa → ΞБb → ΝБc → ΜБd → ΛБe → ΚБf → ΙБg → ΘБh → ΗБi → ΖБj → ΕБk → ΔБl → ΓБm → ΒБn → ΑБo → zБp → yБq → xБr → wБs → vБt → uБu
44 max stepsv000 → uББu → utuv → 1ББА → А0А2
543 max steps30000 → 2БББω → ω1Бω3 → АυБ52 → ωτБ63 → ψςБ84 → χοБB5 → φλБF6 → υζБK7 → τΩБQ8 → σΡБX9 → ςΙБfA → ρzБoB → πpБyC → οnБΑD → ξoБzE → νmБΒF → μnБΑG → λlБΓH → κmБΒI → ιkБΔJ → θlБΓK → ηjБΕL → ζkБΔM → εiБΖN → δjБΕO → γhБΗP → βiБΖQ → αgБΘR → ΩhБΗS → ΨfБΙT → ΧgБΘU → ΦeБΚV → ΥfБΙW → ΤdБΛX → ΣeБΚY → ΡcБΜZ → ΠdБΛa → ΟbБΝb → ΞcБΜc → ΝaБΞd → ΟZБΟb → ΠcБΜa → ΟcБΜb
6232 max stepsf000ιι → ιιeΚIJ → ΟΞUΥbb → pdbΝΜΑ → bYAπΡΟ → ζicΜΗM → ΘZNγΠi → ΔgOβΙm → ΒSGκΨo → ΣuCξuY → βiББΖQ → αΗJηiR → ΜxNγre → ΔX5υΣm → πkGκΕC → δΣJηXO → ΜΔjΕle → XLHιζΤ → ΠΙkΔga → fSIθΨΛ → ΞuUΥuc → paББΞΑ → ΟzCξpb → βd9ρΜQ → θzXΡpK → Μj9ρΖe → θXLεΣK → ΜΘjΕhe → XQKζαΤ → ΚykΔqg → TJ7σθΨ → μΝsvcG → Υa2ψΟW → φndΛΒ6 → πXDνΣC → δΩjΕRO → ΔwKζsm → ΚH3χκg → τΡSΧY8 → μthΗvG → ΥP1ωβW → ψΑmΒo4 → τFBομ8 → μδΥUNG → ΥΕozkW → nKAπηΓ → ζΛEμeM → ΧΘVΤhU → rnPαΒy → zE6τνq → ξΨ8ςSE → κΩtuRI → Πw0Аsa → Аf3χΚ2 → ψτTΦ74 → τνqxE8 → μΨ6τSG → ξΥtuVE → Ωo0АΑS → АvBοt2 → ψδ1ωN4 → ψτΔk74 → τνIθE8 → μΨΝbSG → ΥuaΞuW → ncББΜΓ → ΝΒ8ςnd → κZDνΠI → ΩΠfΙZS → vgSΧΙu → tS0АΨw → Аu2ψu2 → ψυББ54 → χφ2ψ55 → φςπA96 → πιεLIC → δΟΗhaO → ΔeOβΛm → ΒWGκΤo → ΣmCξΓY → βjFλΖQ → ΥzLεpW → Θn9ρΒi → θPDνβK → ΩΜzodS → vYAπΡu → ζi0АΗM → АΘNγh2 → ψΔPαl4 → τzHιp8 → μΠ9ρZG → θΥfΙVK → ΜoSΧΑe → tXBοΣw → δk2ψΕO → φΔJηl6 → πΜHιdC → δΠXΡZO → ΔjfΙΖm → TMGκεΨ → ΣΗsviY → jO2ψγΗ → φΓMδm6 → πΖFλjC → δΥLεVO → ΘΔnΑli → PICξιγ → βΟΑnaQ → zeCξΛq → βW8ςΤQ → κzlΓpI → ΠH9ρκa → θΡeΚYK → ΜiUΥΗe → pXNγΣΑ → ΔkAπΕm → ζKGκηM → ΣΛΗheY → jWOβΤΗ → ΒmMδΓo → ΖGCξλk → βΤKζWQ → ΚzlΓpg → TH9ρκΨ → θΡsvYK → Μi2ψΗe → φXNγΣ6 → πΔjΕlC → δLHιζO → ΠΙΓlga → fSGκΨΛ → ΣuUΥuY → piББΖΑ → Ηz4φpj → ςN9ρδA → ιηΔkKJ → ΞΛIθec → ΞbVΤΞc → ncaΞΝΓ → daEμΟΝ → ΧeYΠΛU → rhVΤΘy → nQ6ταΓ → ξyEμqE → ΩΧ7σTS → μvrwtG → Υ51ωφW → ψρmΒA4 → τηEμK8 → μΧΚeTG → ΥsUΥwW → pn3χΒΑ → τEAπν8 → μζΧSLG → ΥΙsvgW → nS2ψΨΓ → φuEμu6 → πΦББTC → οΧIθTD → βΞrwbQ → zc4φΝq → ςa8ςΟA → κθdΛJI → ΠΝWΣca → lfZΟΚΕ → fUIθΦΛ → ΞqUΥyc → pb7σΞΑ → μcAπΝG → ζΥZΟVM → ΘoeΚΑi → VPBοβΦ → δΑozoO → ΔCAποm → ζγGκOM → ΣΘΒmhY → jQEμαΗ → ΧyMδqU → Ζr7σxk → μL5υζG → πΥΘgVC → δoQΩΑO → ΔxBοrm → δH5υκO → πΡΓlYC → δiGκΗO → ΣΔNγlY → ΔjHιΖm → ΠMGκεa → ΣΗeΚiY → jVNγΥΗ → ΔoMδΑm → ΖHBοκk → δΡKζYO → ΚΔhΗlg → TPHιβΨ → ΠΑsvoa → fC2ψοΛ → φγUΥO6 → πΓozmC → δGAπλO → ζΤΓlWM → ΘmGκΓi → ΣPFλβY → ΥΑiΖoW → nNBοδΓ → δΕEμkO → ΧΔJηlU → ΜrHιxe → ΠX5υΣa → πkeΚΕC → δVJηΥO → ΜΔnΑle → XICξιΤ → βΟkΔaQ → zeIθΛq → ΞW8ςΤc → κmaΞΓI → ΠdFλΜa → ΥfXΡΚW → njTΦΖΓ → rMEμεy → ΧΗ6τiU → ξrNγxE → ΩΔ5υlS → πvHιtC → δΠ1ωZO → ψΔfΙl4 → τTHιΧ8 → μΠrwZG → Υg4φΙW → ςnRΨΒA → θvDνtK