Base 134: Cycles Sequences: Maximum Length Cycle Count

Blog: The First Pixel: Kaprekar's Constant 6174

Radix Character Encoding
0123456789ABCDEF
GHIJKLMNOPQRSTUV
WXYZabcdefghijkl
mnopqrstuvwxyzΑΒ
ΓΔΕΖΗΘΙΚΛΜΝΞΟΠΡΣ
ΤΥΦΧΨΩαβγδεζηθικ
λμνξοπρςστυφχψωА
БВГДЕЖЗИЙКЛМНОПР
СТУФХЦЧШЩЪЫЬЭЮЯа

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 # Full Cycles
(excluding zero)
Max Cycle
Length
Longest Full Cycles
(excluding zero)
(bold = exactly one cycle [excluding zero])
10 cycles--
27 cycles36 nodes0Ц → Х1 → У3 → П7 → ЗF → ρV → ΙΒ → 6Р → ЙD → υR → Ρt → MА → γj → gζ → mΩ → aμ → yΜ → CК → χP → Φp → Uς → Λz → AМ → БL → εh → kβ → eθ → qΥ → Sτ → Οv → IД → λb → wΞ → GЖ → οX → ΕΖ
31 cycle (fixed) 1 node ΕЦΖ
416 cycles33 nodesE9МЙ → ГτRK → ιΠte → sLАΤ → εPφi → Φjβq → gTςη → ΝnΧy → YDИο → υΔΖS → Ρ1Фu → УLА4 → Пδh8 → ЗjβG → ρfζW → ΙnΧΓ → Y5Рο → ЛΔΖC → ω1ФO → УΩl4 → Пbκ8 → ЗvΞG → ρHДW → νΘΒa → Α5РΛ → Л9МC → ГψNK → ιΩle → sbκΤ → wPφΟ → ΦHДq → νTςa → ΝzΚy
52 cycles4 nodesδhЦδj → εhЦδi → εjЦβi → δiЦγj
613 cycles393 nodesKH1ФЕГ → УξθdY4 → ПΔrΣΗ8 → ЗQ2УφG → СρΤqV6 → ЛΚRτΑC → ωΡ8НtO → ЕαMωlI → νγcιja → ΑugεΠΛ → mL9МБα → ГζbκgK → ιwmΨΞe → saGЕμΤ → οzPφΛY → ΦΕAЛΖq → БU0ХςM → ХεΛyh2 → УlBКα4 → ПωcιN8 → ЗβtΠkG → ρfLАηW → εΙoΦΒi → kW6Пπγ → ЙΘfζΓE → υo4СΧS → НΡWοtA → ГΗMωΔK → ιγ2Уje → СsgεΣ6 → ЛmOχΩC → ωΨaλnO → αyYνΜm → ΓcCЙκΙ → χv5РΟQ → ЛΦIГpC → ωλUρbO → αΛwΝzm → cGAЛЖλ → БπvΞWM → εΘHДΓi → νk4Сβa → НΑeηΚA → Гq8НΥK → ЕιSσdI → νΟsΡva → ΑOIГψΛ → λΩ9Мmc → ГwaλΞK → ιyGЕΜe → οsCЙΣY → χΕOχΖQ → ΨΦ0Хpo → ХYUρξ2 → УΛΓΗz4 → ПB3ТЛ8 → ПЗωMF8 → ЗςβjUG → ρΜfζyW → ΙoCЙΧΓ → χX5РοQ → ЛΦΕΕpC → ωUЦЦρO → ψς7ОUP → ЗΨΛynG → ρZBКνW → ωΙΑΙΒO → α86ПОm → ЙЖbκGE → υπvΞWS → ΡΘHДΓu → νM4САa → НδzΚiA → Гj9МγK → ГιgεdK → ιtlΩΡe → scMωκΤ → γvPφΟk → ΦgIГζq → λnTςΨc → ΝwYνΞy → ΓHDИЕΙ → υξ5РYS → ЛΡΓΗtC → ωN3ТωO → ПβΩlk8 → ЗfbκηG → ρwoΦΞW → ΙWGЕπΓ → οΘ5РΓY → ЛΕ4СΖC → Нω0ХNA → ХГαkJ2 → Уκdθc4 → ПvrΣΟ8 → ЗQIГφG → ρλΤqbW → ΙxRτΝΓ → ΡF5РЗu → ЛςLАUC → ωεΛyhO → αlBКαm → ωdbκιO → αwsΡΞm → cOGЕψλ → οΩvΞmY → ΕbHДλΗ → νx1ФΝa → УΑEЗΚ4 → Пσ8НT8 → ЗЕΝwHG → ρξFЖYW → ρΙΓΗΒW → Ι73ТПΓ → ПИ5РE8 → ЛЗσSFC → ωςΞvUO → αΜHДym → νcCЙκa → χΑuΟΚQ → ΦK8НВq → ЕθTςeI → νΝqΤxa → ΑSEЗτΛ → σΠ9МuU → ГΝKБxK → ιηEЗfe → σsoΦΣU → ΝWOχπy → ΨΘDИΓo → υY4СξS → НΡΓΗtA → ГN3ТωK → Пιαkd8 → ЗtdθΡG → ρsMωΣW → γΙOχΒk → Ψg6Пζo → ЙnXξΨE → υΕYνΖS → ΡΓ0ХΘu → ХM4СА2 → УНγi94 → ПДhδI8 → ЗμjβaG → ρzfζΛW → ΙoAЛΧΓ → БX5РοM → ЛεΕΕhC → ωkЦЦαO → ψβNψkP → αΨeηnm → qcYνκΦ → ΓvTςΟΙ → ΝJ5РГy → ЛκDИcC → ωυuΟRO → αΣJВsm → ιcOχκe → ΨvrΣΟo → YQIГφο → λΥΔΖqc → wT1ФσΟ → УΞHДw4 → ПνGЕZ8 → ЗοΑΙXG → ρΖ7ОΕW → ЗΙ0ХΒG → Хρ6ПV2 → УЙΙΑD4 → Пφ7ОQ8 → ИЖΤqGF → σπRτWU → ΡΝΗΓxu → MF3ТЗБ → ПςδhU8 → ЗΜjβyG → ρgCЙζW → χΙmΨΒQ → Φa6Пμq → ЙzTςΛE → υΝAЛxS → БΡEЗtM → σεMωhU → γΝkαxk → geEЗθη → σrnΧΤU → ΝYQυξy → ΤΔDИΗs → υQ2УφS → СΥΠtq6 → ЛTLАσC → ωεΝwhO → αlFЖαm → ρdbκιW → ΙwsΡΞΓ → OH5РЕω → ЛξΩlYC → ωΔbκΗO → αw2УΞm → СcGЕκ6 → ЛοuΟXC → ωΖJВΕO → ια0Хle → ХscιΣ2 → УuOχΠ4 → ПΨKБn8 → ЗηYνfG → ρΓoΦΘW → ΙW4СπΓ → НΘ5РΓA → ЛГ4СJC → НωιcNA → ГβtΠkK → ιfLАηe → εsoΦΣi → kWOχπγ → ΨΘfζΓo → oY4СξΨ → НΔXξΗA → ГΕ2УΖK → Сι0Хd6 → ХЛsΡB2 → УАNψM4 → ПδΩli8 → ЗjbκγG → ρwgεΞW → ΙmGЕΩΓ → οb5РλY → ЛΕwΝΖC → ωG0ХЖO → ХπΩlW2 → УΘbκΓ4 → Пw4СΞ8 → НЗGЕFA → ГςξXUK → ιΜΔΖye → sD1ФЙΤ → УφPφQ4 → ПΦΤqp8 → ЗVRτρG → ρΡΙΑtW → ΙN7ОωΓ → Зβ5РkG → ЛρeηVC → ωΚpΥΑO → αU8Нςm → ЕΜbκyI → νwCЙΞa → χΑGЕΚQ → οΦ8НpY → ЕΕUρΖI → νΛ0Хza → ХΑAЛΚ2 → УБ8НL4 → ПЕεgH8 → ЗξlΩYG → ρΔbκΗW → Ιw2УΞΓ → СH5РЕ6 → МКνYCB → БψΒΘOM → εΩ5Рmi → ЛkaλβC → ωyeηΜO → αqCЙΥm → χcSσκQ → ΦΟuΟvq → UKIГВσ → λθΜxec → wrDИΤΟ → υRHДυS → νΣΠtsa → ΑPLАχΛ → εΧ9Мoi → ГkWοβK → ιΗeηΔe → sq2УΥΤ → СTPφσ6 → ЛΦΝwpC → ωVFЖρO → ραΙΑlW → Ιd7ОιΓ → Зt5РΡG → ЛρMωVC → ωγΙΑjO → αh7Оεm → ЗlbκαG → ρwcιΞW → ΙuGЕΠΓ → οL5РБY → ЛζΔΖgC → ωn1ФΨO → УαYνl4 → ПΓcιΘ8 → Зu4СΠG → НρKБVA → ГηΙΑfK → ιp7ОΦe → ЗsUρΣG → ρΛOχzW → ΨΙAЛΒo → БY6ПξM → ЙεΓΗhE → υl3ТαS → ПΡcιt8 → ЗuMωΠG → ργKБjW → ηΙgεΒg → om6ПΩΨ → ЙbXξλE → υΕwΝΖS → ΡG0ХЖu → ХπLАW2 → УεΗΓh4 → Пl3Тα8 → ПЗcιF8 → ЗςtΠUG → ρΜLАyW → εΙCЙΒi → χk6ПβQ → ЙΦeηpE → υqUρΥS → ΡΛSσzu → ΟMAЛАw → БδHДiM → νεiγha → ΑlhδαΛ → kd9Мιγ → ГtfζΡK → ιoMωΧe → γsWοΣk → ΗgOχζΕ → Ψn1ФΨo → УZXξν4 → ПΕΑΙΖ8 → З80ХОG → ХЖπVG2 → УπΘΒW4 → ПΘ5РΓ8 → ЛЗ4СFC → НωρUNA → ГβΚzkK → ιf9Мηe → ГsoΦΣK → ιWOχπe → ΨΘrΣΓo → YQ4Сφο → НΥΔΖqA → ГT1ФσK → УιΝwd4 → ПtFЖΡ8 → ЗρMωVG → ργΙΑjW → Ιh7ОεΓ → Зl5РαG → ЛρcιVC → ωΚtΠΑO → αM8НАm → ЕδbκiI → νwiγΞa → ΑiGЕδΛ → οj9МγY → ГΕgεΖK → ιm0ХΩe → ХsaλΣ2 → УyOχΜ4 → ПΨCЙn8 → ЗχYνPG → ρΧΒΘoW → ΙX5РοΓ → ЛΖ5РΕC → Лω0ХNC → ХωαkN2 → Уβdθk4 → ПseηΣ8 → ЗqOχΥG → ρΨSσnW → ΟΙYνΒw → ΓI6ПДΙ → Йμ5РaE → ЛυyΛRC → ωΣBКsO → ωαOχlO → αΨcιnm → ucYνκΡ → ΓvLАΟΙ → εJ5РГi → ЛκjβcC → ωvfζΟO → αoIГΧm → λcWοκc → ΗwuΟΞΕ