Base 115: 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
24 max steps10 → 0Г → В1 → А3 → φ7
358 max steps100 → 0ГГ → ВГ1 → БГ2 → АГ3 → ωГ4 → ψГ5 → χГ6 → φГ7 → υГ8 → τГ9 → σГA → ςГB → ρГC → πГD → οГE → ξГF → νГG → μГH → λГI → κГJ → ιГK → θГL → ηГM → ζГN → εГO → δГP → γГQ → βГR → αГS → ΩГT → ΨГU → ΧГV → ΦГW → ΥГX → ΤГY → ΣГZ → ΡГa → ΠГb → ΟГc → ΞГd → ΝГe → ΜГf → ΛГg → ΚГh → ΙГi → ΘГj → ΗГk → ΖГl → ΕГm → ΔГn → ΓГo → ΒГp → ΑГq → zГr → yГs → xГt → wГu → vГv
44 max stepsw000 → vГГv → vuvw → 1ГГВ → В0В2
544 max steps10009 → 90ГВυ → ГςГA1 → ВςГA2 → БρГB3 → АοГD4 → ωμГG5 → ψθГK6 → χγГP7 → φΦГV8 → υΞГc9 → τΖГkA → σwГtB → ςmГΔC → ρsГxD → πlГΕE → οrГyF → ξkГΖG → νqГzH → μjГΗI → λpГΑJ → κiГΘK → ιoГΒL → θhГΙM → ηnГΓN → ζgГΚO → εmГΔP → δfГΛQ → γlГΕR → βeГΜS → αkГΖT → ΩdГΝU → ΨjГΗV → ΧcГΞW → ΦiГΘX → ΥbГΟY → ΤhГΙZ → ΣaГΠa → ΡgГΚb → ΠZГΡc → ΣdГΝa → ΡdГΝb → ΠcГΞc → ΟcГΞd → ΟaГΠd
6252 max steps6000ГГ → ГГ5χ01 → ГВρB11 → ВБεN22 → АωΕl44 → φυIκ88 → ξνΟbGG → ΧΦcΞWW → poaΠΓΓ → fECποΝ → δαWΥSQ → ΒwmΔuq → HB1Бςν → АηΤXM4 → φΙkΖi8 → ξQKθγG → ΧΜzqfW → pW8τΦΓ → μoCπΓI → δΣDοZQ → βΒhΙpS → xRBρβu → ζy2АsO → ψΖ5χl6 → σρJιCB → θεΝdOM → ΚΕYΣmi → jRHλβΙ → ΣyOδsa → Δh5χΚo → ςSEξαC → ζΩvuTO → Ζu0Вwm → ВJ1Бκ2 → БωΞc43 → ψυaΠ86 → ςνeΜGC → ζΦWΥWO → ΖomΔΓm → JHDομλ → βΤΟbYS → xkcΞΗu → bM2АηΡ → ψΙeΜi6 → ςXPγΥC → ζΒlΕpO → ΖJBρκm → ζΟIκcO → ΠΖbΟlc → ecJιΟΞ → ΞcYΣΟe → jcYΣΟΙ → jcOδΟΙ → ΔcOδΟo → ΔcEξΟo → ΩcEξΟU → ΩtbΟxU → td3ωΞy → φa4ψΡ8 → τξfΛFA → κΨUΧUK → Ξsqzye → Z95χτΤ → ςλiΘIC → ζΡOδaO → ΖΔfΛnm → VJFνκΨ → ΧΟqzcW → pc8τΟΓ → μcCπΟI → δΣbΟZQ → ΒicΞΙq → bQAςγΡ → θΑeΜqM → ΚX9σΥi → κmQβΕK → ΞzHλre → ΣZ7υΣa → ξigΚΙG → ΧTPγΩW → ΒuoΒwq → DB1Бςρ → АηγPM4 → φΙΑpi8 → ξQAςγG → θΧzqVM → Κq8τΑi → μR9σβI → κΣxsZK → Ξi4ψΙe → τZPγΣA → κΒhΙpK → ΞRBρβe → ζyYΣsO → Ζj5χΘm → ςOIκεC → ζΠΔmbO → ΖeGμΝm → ΥYIκΤY → ΠljΗΖc → dNJιζΟ → ΞΗaΠke → fZLηΣΝ → ΚiWΥΙi → nRPγβΕ → ΒyGμsq → ΥB5χςY → ςηkΖMC → ζΙKθiO → ΜΖPγlg → ΒVJιΧq → ΞqAςΑe → θZ9σΣM → κΚhΙhK → ΞSQβαe → zwYΣus → j71БφΙ → АοOδE4 → φαΓnS8 → ξwEξuG → ΩΧ1БVU → АtpΑx4 → φB3ως8 → φξζMF8 → ξΨΗjUG → ΧsMζyW → Θp5χΒk → ςNBρζC → ηεΖkON → ΘΕKθmk → ΜNHλζg → ΣΗUΧka → rhLηΚΑ → ΚS8ταi → μwQβuI → Σz1Бra → Аh7υΚ4 → φξRαF8 → ξΨwtUG → Χs2АyW → ψp5χΒ6 → σρBρCB → θζδONM → ΚΗΓnki → RMEξηγ → ΩΙyriU → tQ6φγy → πΑ4ψqE → τβ9σRA → λιxsKJ → ΠΝ4ψec → τdXΤΞA → κlZΡΖK → ΞhJιΚe → ΞZRαΣe → xiYΣΙu → jQ2АγΙ → ψΑOδq6 → ςΔ9σnC → κζFνNK → ΧΞΖkdW → paKθΡΓ → ΜgCπΛg → δVTΨΧQ → ΒtpΑxq → CA3ωσς → φιεNK8 → ξΝΕleG → ΧYIκΤW → ΠpjΗΒc → dNBρζΟ → ζΗaΠkO → ΖfLηΜm → ΚWIκΦi → ΠoQβΓc → zdDοΞs → βa6φΡS → πxfΛtE → βV3ωΧS → φxpΑt8 → ξB3ωςG → φηΦVM8 → ξΙoΒiG → ΧQCπγW → δΑoΒqQ → ΒD9σπq → κγAςQK → θΞzqdM → Κa8τΡi → μgQβΛI → ΣzTΨra → th7υΚy → ξS4ψαG → τΧvuVA → κq0ВΑK → ВΞ9σd2 → АκZΡJ4 → φΟgΚc8 → ξcSΩΟG → ΧvbΟvW → pcГГΞΓ → ΟΒAςpd → θbBρΠM → ζΚdΝhO → ΖZRαΣm → xiIκΙu → ΠQ2Аγc → ψΑcΞq6 → ςb9σΠC → κζdΝNK → ΞΗYΣke → jZLηΣΙ → ΚiOδΙi → ΔRPγβo → ΒyEξsq → ΩB5χςU → ςηsxMC → ζΙ4ψiO → τΖPγlA → κΒJιpK → ΟΝBρed → ζbXΤΠO → ΖldΝΖm → ZKIκιΤ → ΠΝiΘec → dYOδΤΟ → ΔkaΠΗo → fMEξηΝ → ΩΙWΥiU → tnPγΔy → ΒG4ψνq → τΦAςWA → κθnΓLK → ΞΛEξge → ΩZTΨΣU → ushΙyx → R62Аχγ → ψρyrC6 → ςε6φOC → πζΔmNE → βΗGμkS → ΥxLηtY → Κl3ωΖi → φRJιβ8 → ξΞxsdG → Χa4ψΡW → τpfΛΒA → κVBρΧK → ζΞpΑdO → ΖaAςΡm → θgIκΛM → ΠΚTΨhc → tdRαΞy