Base 99: 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 → 0ν → μ1 → κ3 → ζ7
350 max steps100 → 0νν → μν1 → λν2 → κν3 → ιν4 → θν5 → ην6 → ζν7 → εν8 → δν9 → γνA → βνB → ανC → ΩνD → ΨνE → ΧνF → ΦνG → ΥνH → ΤνI → ΣνJ → ΡνK → ΠνL → ΟνM → ΞνN → ΝνO → ΜνP → ΛνQ → ΚνR → ΙνS → ΘνT → ΗνU → ΖνV → ΕνW → ΔνX → ΓνY → ΒνZ → Ανa → zνb → yνc → xνd → wνe → vνf → uνg → tνh → sνi → rνj → qνk → pνl → oνm → nνn
44 max stepso000 → nννn → nmno → 1ννμ → μ0μ2
541 max steps30000 → 2νννλ → λ1νλ3 → μην52 → λζν63 → κδν84 → ιανB5 → θΦνF6 → ηΠνK7 → ζΚνQ8 → εΓνX9 → δuνfA → γlνoB → βeνvC → αkνpD → ΩdνwE → ΨjνqF → ΧcνxG → ΦiνrH → ΥbνyI → ΤhνsJ → ΣaνzK → ΡgνtL → ΠZνΑM → ΟfνuN → ΞYνΒO → ΝeνvP → ΜXνΓQ → ΛdνwR → ΚWνΔS → ΙcνxT → ΘVνΕU → ΗbνyV → ΖUνΖW → ΗYνΒV → ΖXνΓW → ΕXνΓX → ΔWνΔY → ΕUνΖX → ΗXνΓV → ΖYνΒW → ΕWνΔX
6122 max stepsX000ΙΙ → ΙΙWΔST → gfWΔvv → XGEΧΦΕ → ΘΕWΔWU → dYWΔΓy → XUKΠΗΕ → vcWΔyg → XMEΧΟΕ → ΘsWΔiU → dX9γΔy → ΣWKΠΕK → xvXΓfe → VJFΦΣΗ → ΖyazcW → ZPLΟΜΓ → tmSΘoi → fB1λβw → κΟGΥM4 → ζΔriX8 → ΧW8δΕG → ΥΖXΓVI → ΒaUΖΑa → bRPΛΚΑ → liOΜsq → nA4θγo → δΡ0μKA → μΣveJ2 → κyGΥc4 → ζΔLΟX8 → ΧtVΕhG → ΖZBαΒW → ΞZRΙΒO → phRΙtm → hC2καu → θΝCΩO6 → βΜnmPC → Ξm0μoO → μp1λl2 → λι3ι43 → θζδ876 → βΨΤHEC → ΞΙΑZSO → pgQΚum → jE2κΨs → θΙ8δS6 → βΥfuHC → ΞΓEΧYO → ΘpTΗlU → ec3ιyx → ζMIΣΟ8 → ΧzribG → ΖO8δΝW → ΥoYΒmI → ΒT1λΘa → κeQΚw4 → ζjHΤr8 → ΧΒ7εZG → ΧΖRΙVG → ΖhZΑtW → ZRBαΚΓ → ΞiSΘsO → pf9γvm → ΣG2κΦK → θΕwdW6 → βYIΣΓC → ΞzTΗbO → pdNΝxm → pK2κΡm → θw2κe6 → θβHΤB6 → βΟΑZMC → ΞsQΚiO → pj9γrm → Σ82κεK → θΦwdG6 → βΕIΣWC → ΞzXΓbO → pVNΝΖm → pa2κΑm → θQ2κΛ6 → θβjqB6 → βΟ6ζMC → ΩΞriNE → Κq8δkS → Υh5ηtI → βΒBαZC → ΟΝRΙON → rogtmk → D71λζα → κΨΛPE4 → ζΙkpS8 → Χg4θuG → δΖDΨVA → ΣΚZΑRK → xiQΚse → jJ9γΣs → Σy8δcK → ΥxLΟdI → ΒtJΡha → xRBαΚe → ΞiIΣsO → zp9γlc → ΣN3ιΞK → ζxpkd8 → ΧK4θΡG → δΖveVA → ΣaGΥΑK → ΔxPΛdY → lVJΡΖq → xa4θΑe → δQIΣΛA → ΣzjqbK → xO6ζΝe → ΩoIΣmE → Κz1λbS → κhNΝt4 → ζpBαl8 → ΧΞ3ιNG → ζΖpkV8 → Χa4θΑG → δΖPΛVA → ΣlZΑpK
751 max steps1000033 → 330νμκλ → νιην541 → μιγν942 → λθΨνD53 → κζΣνI74 → ιγΛνPA5 → θΨΑνZE6 → ηΣmνnJ7 → ζΜUνΖP8 → εΕgνtW9 → δwNνΝeA → γΕXνΓWB → βuWνΔgC → αtMνΞhD → ΩΓVνΕYE → ΨsVνΕiF → ΧrLνΟjG → ΦΑUνΖaH → ΥqUνΖkI → ΤpKνΠlJ → ΣyTνΗcK → ΡoTνΗmL → ΠnJνΡnM → ΣuRνΙgK → ΡqRνΙkL → ΠpNνΝlM → ΟsQνΚiN → ΞoQνΚmO → ΝnMνΞnP → ΟoOνΜmN → ΞqOνΜkO → ΝpQνΚlP → ΜmNνΝoQ → ΞmOνΜoO → ΝpOνΜlP → ΝnPνΛnP → ΜnMνΞnQ → ΟnNνΝnN → ΞrOνΜjO → ΝpRνΙlP → ΜlMνΞpQ → ΟnPνΛnN → ΞpMνΞlO → ΟpRνΙlN → ΞnMνΞnO → ΟpPνΛlN → ΞpOνΜlO → ΝpPνΛlP → ΜnOνΜnQ → ΝlNνΝpP → ΞnQνΚnO