Base 107: 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
24 max steps10 → 0υ → τ1 → ς3 → ξ7
354 max steps100 → 0υυ → τυ1 → συ2 → ςυ3 → ρυ4 → πυ5 → ου6 → ξυ7 → νυ8 → μυ9 → λυA → κυB → ιυC → θυD → ηυE → ζυF → ευG → δυH → γυI → βυJ → αυK → ΩυL → ΨυM → ΧυN → ΦυO → ΥυP → ΤυQ → ΣυR → ΡυS → ΠυT → ΟυU → ΞυV → ΝυW → ΜυX → ΛυY → ΚυZ → Ιυa → Θυb → Ηυc → Ζυd → Ευe → Δυf → Γυg → Βυh → Αυi → zυj → yυk → xυl → wυm → vυn → uυo → tυp → sυq → rυr
44 max stepss000 → rυυr → rqrs → 1υυτ → τ0τ2
541 max stepsq0000 → pυυυt → toυtq → u2υςp → σpυs3 → ςqυr4 → ρoυt5 → πpυs6 → οnυu7 → ξoυt8 → νmυv9 → μnυuA → λlυwB → κmυvC → ιkυxD → θlυwE → ηjυyF → ζkυxG → εiυzH → δjυyI → γhυΑJ → βiυzK → αgυΒL → ΩhυΑM → ΨfυΓN → ΧgυΒO → ΦeυΔP → ΥfυΓQ → ΤdυΕR → ΣeυΔS → ΡcυΖT → ΠdυΕU → ΟbυΗV → ΞcυΖW → ΝaυΘX → ΜbυΗY → ΛZυΙZ → ΚaυΘa → ΙYυΚb → ΛXυΛZ → ΜaυΘY → ΛaυΘZ
6209 max steps7000Hξ → ξH6ξδ8 → θζΚYFE → ΣΟaΘUS → pkWΜyu → fE4πηΕ → μΡOΥSA → βvnunK → Ζ86ξνe → θεQΣGE → ΣΝqrWS → pg0τΓu → τM4πΨ2 → ςμzi94 → ξγGδI8 → ζΜΘaXG → ΞeWΜΕW → hfPΤΔΓ → tOKΩΦq → Δw2ςmg → πN9λΧ6 → κβxkJC → ΧΗCθcO → ΥxTΟlQ → tlBιxq → ΧC2ςιO → πΦwlO6 → κwAκmC → ΩΧ9λNM → βΒxkhK → ΖKCθαe → ΥΕQΣeQ → trPΤrq → t2υυςq → σslwq3 → πB1σκ6 → ςκΧMB4 → ξΨyjM8 → ζΑEζiG → ΠΞHγVU → ΚlhΑxa → ZJBιβΛ → ΧΗaΘcO → xXTΟΜm → leAκΕy → ΩQCθΤM → ΥΒrqhQ → tK0ταq → τΕ2ςe2 → ςπPΤ54 → ξλspA8 → ζα2ςKG → πΞΔeV6 → κiOΥΑC → ΧvHγnO → Κx7νla → ζZBιΚG → ΧΞZΙVO → xiYΚΑm → bIAκγΙ → ΩΙWΜaM → ΒfXΛΔi → dOIβΦΗ → ΘwSΠmc → nV9λΞw → βi8μΑK → δΖHγdI → ΛΙRΡaZ → pbXΛΘu → dW4πΝΗ → μgSΠΓA → βnLΨvK → ΖΒ7νhe → ζRJαΣG → ΞΖpsdW → hS2ςΡΓ → πoKΩu6 → κΔ5οfC → κΧNΦNC → ΧywlkO → xEAκηm → ΩΡAκSM → ΩΒnuhM → ΒK6ξαi → θΕIβeE → ΣΘPΤbS → tpVΝtq → h42ςρΓ → πνKΩ86 → κεΓfGC → ΧΝMΧWO → zxfΓlk → NFBιζΨ → ΧΟyjUO → xkEζym → ΠEAκηU → ΩΡkxSM → ΒoCθui → ΥJ5οβQ → κΗspcC → ΧU2ςΟO → πxjyl6 → κFBιζC → ΨΦΞUON → zwizmk → HF9λζε → βΟΛXUK → ΖkcΖye → TRDηΣΡ → ΣqmvsS → p91σμu → ςγ4πI4 → ξμΘa98 → ζγWΜIG → ΞΙeΔaW → hYOΥΛΓ → vcKΩΗo → ΔU6ξΟg → θkMΧyE → ΣzDηjS → ΣpFεtS → Ξp3ρtW → ξh3ρΒ8 → ξζJαF8 → ζΟΕdUG → ΞkQΣyW → rhDηΒs → ΣK0ταS → τΕote2 → ςQ4πΤ4 → ξμrq98 → ζγ0τIG → τΞΘaV2 → ςiWΜΑ4 → ξfHγΔ8 → ζΚNΦZG → ΞxZΙlW → hZBιΚΓ → ΧaKΩΙO → ΔxXΛlg → dNBιΧΗ → ΧySΠkO → xnDηvm → ΣB7νκS → ζΨotMG → ΞΑ4πiW → μhHγΒA → βΚJαZK → ΗΕZΙed → ZTPΤΠΛ → tmaΘwq → XA2ςλΝ → παeΔK6 → κΕOΥeC → ΧvPΤnO → xt7νpm → ζB3ρκG → ξΨΝVM8 → ζΑgΒiG → ΞLHγΩW → ΚΓgΒga → ZMKΩΨΛ → ΔΑaΘig → XNHγΧΝ → ΚyeΔka → ZPDηΥΛ → ΣuaΘoS → pX5οΜu → κe4πΕC → μΧPΤNA → βyspkK → ΖE2ςηe → πΡQΣS6 → κrnurC → Χ6υυξO → οΦFεO7 → θΞvmVE → Σi8μΑS → δpHγtI → ΛΙ3ρaZ → ξbXΛΘ8 → ζdVΝΖG → ΞhRΡΒW → phJαΒu → ΖK4παe → μΕQΣeA → βrPΤrK → Ζsυυpe → ΕtCθpf → ΥP3ρΥQ → ξuspo8 → ζ62ςοG → πιΝVC6 → κΦgΒOC → ΧwKΩmO → Δx9λlg → βNBιΧK → ΧΖxkdO → xSCθΡm → ΥoAκuQ → Ωt5οpM → κΒ3ρhC → ξΧJαN8 → ζΖxkdG → ΞSCθΡW → ΥogΒuQ → tL5οΩq → κΓ2ςgC → πΧLΨN6 → κΒxkhC