Base 123: 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 steps100
29 max steps10 → 0Л → К1 → И3 → Д7φFζVД7
364 max steps100 → 0ЛЛ → КЛ1 → ЙЛ2 → ИЛ3 → ЗЛ4 → ЖЛ5 → ЕЛ6 → ДЛ7 → ГЛ8 → ВЛ9 → БЛA → АЛB → ωЛC → ψЛD → χЛE → φЛF → υЛG → τЛH → σЛI → ςЛJ → ρЛK → πЛL → οЛM → ξЛN → νЛO → μЛP → λЛQ → κЛR → ιЛS → θЛT → ηЛU → ζЛV → εЛW → δЛX → γЛY → βЛZ → αЛa → ΩЛb → ΨЛc → ΧЛd → ΦЛe → ΥЛf → ΤЛg → ΣЛh → ΡЛi → ΠЛj → ΟЛk → ΞЛl → ΝЛm → ΜЛn → ΛЛo → ΚЛp → ΙЛq → ΘЛr → ΗЛs → ΖЛt → ΕЛu → ΔЛv → ΓЛw → ΒЛx → ΑЛy → zЛzyЛΑzЛz
424 max stepsΑ000 → zЛЛz → zyzΑ → 1ЛЛК → К0К2КЗ32ИГ74ДυF8φεVGζwΒWx4ЖΓВ4ЖAВρJAςΦdKΧgΣehaΩΤnaΩΝnOμΝΜOμoΜMξoΠMξkΠUζkzUζΑz0КΑК0К2
551 max steps30000 → 2ЛЛЛЙ → Й1ЛЙ3 → КЕЛ52 → ЙДЛ63 → ИВЛ84 → ЗωЛB5 → ЖυЛF6 → ЕπЛK7 → ДκЛQ8 → ГγЛX9 → ВΤЛfA → БΚЛoB → АzЛyC → ωoЛΚD → ψxЛΑE → χnЛΛF → φwЛΒG → υmЛΜH → τvЛΓI → σlЛΝJ → ςuЛΔK → ρkЛΞL → πtЛΕM → οjЛΟN → ξsЛΖO → νiЛΠP → μrЛΗQ → λhЛΡR → κqЛΘS → ιgЛΣT → θpЛΙU → ηfЛΤV → ζoЛΚW → εeЛΥX → δnЛΛY → γdЛΦZ → βmЛΜa → αcЛΧb → ΩlЛΝc → ΨbЛΨd → ΩiЛΠc → ΨeЛΥd → ΧhЛΡe → ΦdЛΦf → ΧeЛΥe → ΦgЛΣf → ΥdЛΦg → ΧdЛΦe → ΧgЛΣe → ΦeЛΥfΦeЛΥf
6593 max steps1000BВ → ВB0КАA → КςξMJ2 → ИΨΟjc4 → ДkUζΟ8 → φzTηzG → ζΑЛЛxW → εΒSθxX → Δv3ЗΔw → Д86ДГ8 → ψφτGFE → κηγXUS → ΖΑsΖyu → DB1ЙАω → ИολPM4 → ДΡΙpi8 → φYIςγG → ζΩrΗbW → xmEφΝΓ → θQ4ЖλU → ВΙΑxqA → ςI2ИσK → ЖαΦda6 → АogΣΛC → ξbLοΩO → ΣΞlΝli → ZSQκιγ → ΘΕqΘus → HF9Бφυ → ςηγXUK → ΧΑsΖye → hD1ЙψΤ → ИλaΩQ4 → ДΙmΜq8 → φPHσμG → ζβΚoZW → xqKπΙΓ → ΥI4Жσg → ВαcΧaA → ςoiΠΛK → ΧXLοδe → ΣugΣΕi → bZ9Бβα → ςqmΜΙK → ΧPHσμe → βΛgΣoa → pbLοΩΛ → ΣmKπΝi → ΥZPλβg → ΚqcΧΙq → jJHσςΡ → βΨWδca → vpjΟΚΕ → VK8Вρη → τΦyzeI → βg0КΤa → КpbΨΚ2 → ИlJρΞ4 → ДΧRιd8 → φΖhΡtG → ζZBωβW → ξxpΙΒO → ΞJ3Зςm → ДΨQκc8 → φΘjΟrG → ζVFυζW → ζywΒΑW → x51ЙЖΓ → ИБ4ЖA4 → ДВπK98 → φσΤfIG → ζαcΧaW → xoiΠΛΓ → XM4Жοε → ВΡuΔiA → ςY8ВγK → τΧrΗdI → βiEφΡa → θpXγΚU → ΒtJρΖy → ΧC2Иωe → ЖνgΣO6 → АΝaΩmC → ξnPλΜO → ΞΚNνpm → ΞRJρκm → ΧΗQκse → ΘhDχΣs → κaEφαS → θΖnΛtU → ΒNBωξy → ξΟ2ИkO → ЖΞTηl6 → АΒRιxC → ξΖ3ЗtO → ДΞBωl8 → φξRιNG → ζΟΕtkW → xUAАηΓ → πΑ4ЖyM → ВΣ1ЙhA → ИςZαJ4 → ДΨoΚc8 → φkKπΟG → ζΥTηfW → ΒxdΦΒy → h42ИЗΤ → ЖГaΩ86 → АυmΜGC → ξεOμWO → ΞΜvΓnm → RO6Дνλ → ψΝΗrmE → κQEφλS → θΙΕtqU → ΒIAАσy → πα2ИaM → ЖΣnΛh6 → АaMξαC → ξΠnΛjO → ΞWMξεm → ΠwQκΓk → ΘV5Еζs → АyEφΑC → ξθ1ЙTO → ИΞΒwl4 → ДS4Жι8 → ВφΔuFA → ςη8ВUK → τΧzydI → βi0КΡa → КpXγΚ2 → ИtJρΖ4 → ДΧBωd8 → φξhΡNG → ζΟYβkW → xrTηΘΓ → ΒG4Жυy → Вε2ИWA → ЖςvΓJ6 → АΨ6ДcC → ψξjΟNE → κΟUζkS → ΖzTηzu → ΒAЛЛАy → БΑlΝyB → πR1ЙκM → ИΣΖsh4 → ДaCψα8 → φμnΛPG → ζΛMξoW → ΠxLοΒk → ΣV3Зζi → ДyYβΑ8 → φr1ЙΘG → ИζFυV4 → ДζxΑV8 → φy2ИΑG → Жζ1ЙV6 → ИАxΑB4 → Дο2ИM8 → ЖφΠiF6 → АηWδUC → ξΑuΔyO → Ξ91ЙВm → ИσQκI4 → ДαΗra8 → φoEφΛG → θζLοVU → ΣΒxΑxi → Z42ИЗγ → ЖГqΘ86 → АυGτGC → ξεγXWO → ΞwsΖΓm → RD5Еψλ → АλΗrQC → ξΙEφqO → θΞHσlU → βΒRιxa → Ζp3ЗΚu → ДKAАρ8 → φπΥeLG → ζΤeΥgW → xfbΨΥΓ → le4ЖΦΟ → ВgSθΤA → ςΔbΨvK → Χl7ГΞe → φhRιΣG → ζΖZαtW → xpBωΚΓ → ξK4ЖρO → ВΦΝleA → ςgQκΤK → ΧΘbΨre → lhFυΣΟ → ζaSθαW → ΔxnΛΒw → N73ЗДο → ДχΟjE8 → φιUζSG → ζΕyzuW → xA0КБΓ → Кρ4ЖK2 → ИВΥe94 → ДσeΥI8 → φαeΥaG → ζoeΥΛW → xfLοΥΓ → Σe4ЖΦi → ВgYβΤA → ςrbΨΘK → ΧlFυΞe → ζhRιΣW → ΖxZαΒu → pB3ЗАΛ → ДοKπM8 → φΥΠifG → ζeWδΦW → xvfΤΔΓ → d84ЖГΨ → ВυiΠGA → ςεWδWK → ΧwuΔΓe → h95ЕВΤ → АσaΩIC → ξαmΜaO → ΞoOμΛm → ΜRLοκo → ΣΗMξsi → ΠZDχβk → κqUζΙS → ΖzHσzu → βAЛЛАa → БαNνaB → πΞnΛlM → ΣSMξιi → ΠΕYβuk → rV9БζΙ → ςyGτΑK → δΧ1ЙdY → ИthΡΖ4 → ДZBωβ8 → φξpΙNG → ζΟIςkW → ΩxTηΒc → Βl3ЗΞy → ДS2Иι8 → ЖφΔuF6 → Аη8ВUC → τξzyNI → βΟ0Кka → КpTηΚ2 → ИΒJρx4 → ДΧ3Зd8 → ДφhΡF8 → φηYβUG → ζΑqΘyW → xH1ЙτΓ → Иγ4ЖY4 → ДВrΗ98 → φσEφIG → θζΩaVU → ΒymΜΑy → P31ЙИν → ИЕΛn64 → ДωMξC8 → φνΟjOG → ζΝUζmW → zxPλΒΑ → Κ40КЗq → КГIς82 → ИυΨbG4 → ДεkΞW8 → φwSθΓG → ζΔ5ЕvW → Аx7ГΒC → φξ3ЗNG → ДζΞkV8 → φySθΑG → ζΔ1ЙvW → Иx7ГΒ4 → Дφ3ЗF8 → ДφζUF8 → φηyzUG → ζΑ0КyW → Кx1ЙΒ2 → ЙЗ3З43 → ЖДВ876 → АχσHEC → ξιαZSO → ΞΕoΚum → RL9Бπλ → ςΤΗrgK → ΧcEφΨe → θkgΣΟU → ΒbTηΩy → Βm2ИΝy → ЖQ2Иλ6 → ЖАΘqB6 → АοGτMC → ξδΠiXO → ΞuWδΕm → vR9БκΕ → ςΗ8ВsK → τΧDχdI → κβhΡZS → ΖqYβΙu → rIAАσΙ → παGτaM → δΣnΛhY → taMξαΗ → ΠoCψΛk → μVLοζQ → ΣΚxΑpi → ZK2Иργ → ЖΦqΘe6 → АgGτΤC → ξδbΨXO → ΞukΞΕm → TR9Бκι → ςΗΓvsK → ΧE6Дχe → ψιgΣSE → κΕaΩuS → Ζn9БΜu → ςOAАνK → πΧΜmdM → ΣiOμΡi → ΜZXγβo → tqMξΙΗ → ΠICψσk → μαUζaQ → ΚznΛzq → NIЛЛςο → σξ2ИNJ → ЖΩΞkb6 → АmSθΝC → ξΔPλvO → ΞΚ7Гpm → φRJρκG → ζΧΖsdW → xiCψΡΓ → μY4ЖγQ → ВΚrΗpA → ςKEφρK → θΧΥedU → ΒieΥΡy → fY2ИγΦ → ЖseΥΗ6 → АfDχΥC → ξκdΦRO → ΞΗgΣsm → bRDχκα → κΗmΜsS → ΖPDχμu → κΛAАoS → πΖLοtM → ΤΡBωih → ξbXγΩO → ΞtlΝΖm → SQBωλκ → ξΙΕtqO → ΞIAАσm → παQκaM → ΣΘnΛri → ZNFυξγ → ζΟqΘkW → xUGτηΓ → δΑ4ЖyY → Вt1ЙΖA → ИςBωJ4 → ДξΧcN8 → φΟiΠkG → ζXTηδW → ΒxtΕΒy → B42ИЗБ → ЖГοL86 → АυΡhGC → ξεYβWO → ΞwqΘΓm → RH5Еτλ → АγΗrYC → ξsEφΗO → θΞDχlU → κΒRιxS → ΗΕ3Зut → ДD9Бψ8 → φςκQJG → ζΨΗrcW → xkEφΟΓ → θU4ЖηU → ВΒzyxA → ς40КЗK → КГΦd82 → ИυgΣG4 → ДεaΩW8 → φwmΜΓG → ζP5ЕμW → АΛwΒoC → ξM4ЖοO → ВΡΝliA → ςYQκγK → ΧΘrΗre → hGEφυΤ → θεaΩWU → ΒwmΜΓy → P62ИЕν → ЖωΛnC6 → АνMξOC → ξΠΜmjO → ΞWOμεm → ΜwQκΓo → ΘN5Еξs → АΟEφkC → ξθTηTO → ΞΓΑxwm → R62ИЕλ → ЖωΗrC6 → АνEφOC → ξθΜmTO → ΞΓOμwm → ΜR5Еκo → АΗMξsC → ξΠDχjO → κΞVεlS → ΖxRιΒu → ΖB3ЗАu → ДοAАM8 → φπΠiLG → ζΤWδgW → xvbΨΔΓ → l84ЖГΟ → ВυSθGA → ςεΓvWK → Χw6ДΓe → ψh5ЕΣE → АκZαRC → ξΗoΚsO → ΞLDχπm → κΤQκgS → ΘΖbΨts → lFBωφΟ → ξηSθUO → ΞΔzyvm → R80КГλ → КυΗrG2 → ИεEφW4 → ДθvΓT8 → φΓ6ДwG → ψζ5ЕVE → АκxΑRC → ξΗ2ИsO → ЖΞDχl6 → АκRιRC → ξΗΕtsO → ΞEAАχm → πιQκSM → ΣΘΔuri → ZG8Вυγ → τεqΘWI → βwGτΓa → δp5ЕΚY → АtJρΖC → ξΧBωdO → ξΞhΡlO → ΞZRιβm → ΖqQκΙu → ΘIAАσs → παEφaM → θΣnΛhU → ΒaMξαy → Πo2ИΛk → ЖVLοζ6 → АΣxΑhC → ξa2ИαO → ЖΞnΛl6 → АSMξιC → ξΠΔujO → ΞW8Вεm → τwQκΓI → βΘ5Еra → АpFυΚC → ξζJρVO → ΧΞxΑle → hS2ИιΤ → ЖΕaΩu6 → Аn9БΜC → ςξNνNK → ΧΟΝlke → hUQκηΤ → ΘΑaΩys → nF1ЙφΝ → ИηOμU4 → ДΜzyn8 → φO0КνG → КζΜmV2 → ИyOμΑ4 → ДΜ1Йn8 → ИφNνF4 → ДηΝlU8 → φΑQκyG → ζΘ1ЙrW → ИxFυΒ4 → Дζ3ЗV8 → ДφxΑF8 → φη2ИUG → ЖζzyV6 → Аy0КΑC → Кξ1ЙN2 → ЙЗΞk43 → ЖГSθ86 → АυΓvGC → ξε6ДWO → ψΞvΓlE → κS6ДιS → ψΖΔutE → κC8ВωS → τνΕtOI → βΝAАma → πpPλΚM → ΣΚJρpi → ΧZJρβe → ΧqgΣΙe → hbHσΩΤ → βmaΩΝa → pnPλΜΛ → ΚOKπνq → ΥΝIςmg → ΩdPλΧc → ΚlhΡΞq → ZSIςιγ → ΩΕqΘuc → lH9БτΟ → ςγSθYK → ΧΔrΗve → hF7ГφΤ → φηaΩUG → ζΑmΜyW → xP1ЙμΓ → ИΛ4Жo4 → ДВLο98 → φσΡhIG → ζαYβaW → xrnΛΘΓ → NG4Жυο → ВεΟjWA → ςwUζΓK → Χz5Еze → АgЛЛΣC → ωΤVεgD → μxbΨΒQ → Κl3ЗΞq → ДSIςι8 → φΩΔubG → ζm8ВΝW → τxPλΒI → βΚ3Зpa → ДpJρΚ8φΧJρdGζΧhΡdWxiYβΡΓrY4ЖγΙВsGτΗAςδDχXKκΧtΕdSΖiAАΡuπYAАγMπΣrΗhMΣaEφαiθoYβΛUΒrLοΘyΣG2ИυiЖεYβW6АwqΘΓCξH5ЕτOАγΝlYCξsQκΗOΞΘDχrmκRFυκSζΗΕtsWxEAАχΓπι4ЖSMВΣΔuhAςa8ВαKτΧnΛdIβiMξΡaΠpXγΚktVJρζΗΧyCψΑeμh1ЙΣQИΚZαp4ДpJρΚ8