Base 113: 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 steps1 → 0 → 0
212 max steps10 → 0Б → А1 → ψ3 → τ7 → μF → ΥV → nΒ → Dξ → ΩR → vt → 1А → ψ3
359 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 → tБv → uБu
418 max stepsv000 → uББu → utuv → 1ББА → А0А2 → Аχ32 → ψσ74 → τλF8 → μΤVG → ΥmΒW → nEμΓ → ΧEμU → ΧqxU → r6τy → ξ6τE → ξΨRE → ΩutS → v0Аu → А0А2
547 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 → ΞbБΝc → ΞaБΞc → ΟaБΞb → ΟcБΜb
6430 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 → ΩΜ1ωdS → ψvXΡt4 → τj1ωΖ8 → ψμLεF4 → τΦΗhU8 → μqOβyG → ΥΒ7σnW → μnDνΒG → ΩΥDνVS → ΩvnΑtS → vD1ωξu → ψα0АQ4 → Аτxq72 → ψν6τE4 → τξΧSD8 → μαsvQG → Υy2ψqW → φn7σΒ6 → πμDνFC → δΩΥURO → Δwozsm → HB3χπλ → τεΡXM8 → μΗiΖiG → ΥOMδγW → ΖΓmΒmk → LGEμλη → ΧΤΙfWU → rmSΧΓy → tG6τλw → ξΤ2ψWE → φΩlΓR6 → πwGκsC → δΣ3χXO → τΔjΕl8 → μLHιζG → ΥΠΘgZW → ngQΩΙΓ → xSEμΨs → Χu4φuU → ςqББxA → ρyhΗqB → ζP7σβM → μΘzohG → ΥQAπαW → ζymΒqM → ΘF7σμi → μΦOβUG → ΥΒpynW → nE8ςνΓ → κΨEμSI → ΧΠtuZU → rg0АΙy → АS6τΨ2 → ψξtuD4 → τα0АQ8 → АμxqF2 → ψΦ6τU4 → τξpyD8 → μα8ςQG → κΥxqVI → Πo6τΑa → ξfBοΚE → δΩTΦRO → Δwqxsm → H73χτλ → τνΡXE8 → μΨiΖSG → ΥuMδuW → ΖmББΒk → ΕΓ3χml → τJFλθ8 → μΥΜcVG → ΥoYΠΑW → nhBοΘΓ → δQEμαO → ΧΔxqlU → rI6τιy → ξΟ6τaE → ξΩdΛRE → ΩwWΣsS → vl3χΔu → τI0Аι8 → АμΞaF2 → ψΦcΜU4 → τqYΠy8 → μh7σΘG → μΥPαVG → ΥznΑpW → nD9ρξΓ → θαEμQK → ΧΜxqdU → rY6τΡy → ξi6τΗE → ξΩNγRE → ΩΔvslS → vI2ψιu → φΟ0Аa6 → АπdΛB2 → ψεWΣM4 → τΗkΔi8 → μOIθγG → ΥΞΒmbW → ncEμΝΓ → ΧaEμΟU → ΧrdΛxU → rX5υΣy → πk6τΕC → ξδJηNE → ΩΜΔkdS → vYIθΡu → Ξi0АΗc → АbNγΞ2 → ψΔbΝl4 → τbHιΞ8 → μΠbΝZG → ΥgaΞΙW → ndRΨΜΓ → vYEμΡu → Χi0АΗU → АrNγx2 → ψΔ5υl4 → τπHιB8 → μεΟZMG → ΥΗeΚiW → nVNγΥΓ → ΔoEμΑm → ΧHBοκU → δΡqxYO → Δi6τΗm → ξOGκγE → ΩΣΒmXS → vkEμΕu → ΧK0АηU → АΛqxe2 → ψW6τΤ4 → τξlΓD8 → μαGκQG → ΥΣxqXW → nk6τΕΓ → ξKEμηE → ΩΧΚeTS → vsUΥwu → p40АχΑ → АσAπ82 → ψλεLG4 → τΤΗhW8 → μmOβΓG → ΥΒFλnW → ΥnDνΒW → ΩnDνΒS → ΩvDνtS → Ωv1ωtS → ψv1ωt4 → ψτ1ω74 → ψτμE74 → τνΦTE8 → μΨqxSG → Υu6τuW → ξmББΒE → νΓZΟmF → ΧfFλΚU → ΥrTΦxW → rn5υΒy → πE6τνC → ξδΧSNE → ΩΕsvkS → vK2ψηu → φΛ0Аe6 → АπVΤB2 → ψεmΒM4 → τΗEμi8 → μΧNγTG → ΥΔrwlW → nI4φιΓ → ςΟEμaA → θΧdΛTK → ΜsWΣwe → lX3χΣΕ → τkIθΕ8 → μΞJηbG → ΥΜbΝdW → nbXΡΞΓ → jcEμΝΗ → ΧaMδΟU → ΖrdΛxk → XL5υζΤ → πΙkΔgC → δSIθΨO → ΞΔtulc → bI0АιΟ → АΟcΜa2 → ψeYΠΛ4 → τhVΤΘ8 → μnPαΒG → ΥzDνpW → Ωn9ρΒS → θvDνtK