Base 134: Cycles Sequences: All Cycle Counts

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)
Frequency Cycle
Length
Full Cycles
(excluding zero)
(bold = exactly one cycle [excluding zero])
10 cycles---
27 cycles4,788×(max) 36 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
1,596×12 nodes2Ф → С5 → ЛB → ωN → αl → cκ → uΠ → KВ → ηf → oΧ → Wπ → ΗΔ
1,197×9 nodes4Т → Н9 → ГJ → ιd → sΣ → Oψ → Ψn → Yξ → ΓΘ
532×4 nodes8О → ЕH → νZ → ΑΚ
399×3 nodesEИ → σT → Νx
266×2 nodesQφ → Τr
133×(fixed) 1 node 
31 cycle 409,906×(fixed) (max) 1 node ΕЦΖ
416 cycles886,384×(max) 33 nodeskfζγ → ofζΨ → oXξΨ → ΕXξΗ → Ε1ФΗ → У1Ф4 → УО74 → ПЖF8 → ЗπVG → ρΘΒW → Ι5РΓ → Л5РC → ЛψNC → ωΩlO → αbκm → wbκΟ → wHДΟ → νHДa → νzΚa → Α9МΛ → Г9МK → ГθdK → ιrΣe → sPφΤ → ΦPφq → ΦTςq → ΝTςy → ΝDИy → υDИS → υΠtS → ΡLАu → εLАi → εjβi
884,835×(max) 33 nodes61ФС → УКB4 → ПψN8 → ЗΩlG → ρbκW → ΙvΞΓ → I5РЕ → ЛμZC → ωzΚO → α9Мm → ГbκK → ιvΞe → sHДΤ → νPφa → ΦzΚq → U9Мσ → ГΜxK → ιDИe → υrΣS → ΡPφu → ΦLАq → εTςi → Νjβy → gDИη → υnΧS → ΡXξu → ΕLАΗ → ε1Фi → Уjβ4 → Пfζ8 → ЗnΧG → ρXξW → ΙΔΖΓ
884,717×(max) 33 nodesQ9Мχ → ГΥpK → ιTςe → ΝrΣy → QDИχ → υΥpS → ΡTςu → ΝLАy → εDИi → υjβS → Ρfζu → oLАΨ → εXξi → ΕjβΗ → g1Фη → УnΧ4 → ПXξ8 → ЗΔΖG → ρ1ФW → УΘΒ4 → П5Р8 → ЛЖFC → ωπVO → αΘΒm → c5Рλ → ЛvΞC → ωHДO → νΩla → ΑbκΛ → w9МΟ → ГHДK → νθda → ΑrΣΛ
879,400×(max) 33 nodesI9МЕ → ГμZK → ιzΚe → s9МΤ → ГPφK → ιΥpe → sTςΤ → ΝPφy → ΦDИq → υTςS → ΡΜxu → MDИБ → υδhS → Ρjβu → gLАη → εnΧi → kXξγ → ΕfζΗ → o1ФΨ → УXξ4 → ПΔΖ8 → З1ФG → УπV4 → ПΘΒ8 → З5РG → ЛπVC → ωΘΒO → α5Рm → ЛbκC → ωvΞO → αHДm → νbκa → ΑvΞΛ
877,780×(max) 33 nodesI1ФЕ → УμZ4 → ПzΚ8 → З9МG → ГπVK → ιΘΒe → s5РΤ → ЛPφC → ωΥpO → αTςm → Νbκy → wDИΟ → υHДS → νΠta → ΑLАΛ → ε9Мi → ГjβK → ιfζe → snΧΤ → YPφο → ΦΔΖq → U1Фσ → УΜx4 → ПDИ8 → ЗτRG → ρΠtW → ΙLАΓ → ε5Рi → ЛjβC → ωfζO → αnΧm → cXξλ → ΕvΞΗ
877,108×(max) 33 nodesE1ФЙ → УτR4 → ПΠt8 → ЗLАG → ρδhW → ΙjβΓ → g5Рη → ЛnΧC → ωXξO → αΔΖm → c1Фλ → УvΞ4 → ПHД8 → ЗμZG → ρzΚW → Ι9МΓ → Г5РK → ЛθdC → ωrΣO → αPφm → Φbκq → wTςΟ → ΝHДy → νDИa → υzΚS → Ρ9Мu → ГLАK → ιδhe → sjβΤ → gPφη → ΦnΧq → YTςο → ΝΔΖy
877,032×(max) 33 nodesE5РЙ → ЛτRC → ωΠtO → αLАm → εbκi → wjβΟ → gHДη → νnΧa → ΑXξΛ → Ε9МΗ → Г1ФK → Уθd4 → ПrΣ8 → ЗPφG → ρΥpW → ΙTςΓ → Ν5Рy → ЛDИC → ωτRO → αΠtm → cLАλ → εvΞi → kHДγ → νfζa → ΑnΧΛ → Y9Мο → ГΔΖK → ι1Фe → УrΣ4 → ПPφ8 → ЗΥpG → ρTςW → ΝΘΒy
876,522×(max) 33 nodesIDИЕ → υμZS → ΡzΚu → M9МБ → ГδhK → ιjβe → sfζΤ → oPφΨ → ΦXξq → ΕTςΗ → Ν1Фy → УDИ4 → ПτR8 → ЗΠtG → ρLАW → εΘΒi → k5Рγ → ЛfζC → ωnΧO → αXξm → ΕbκΗ → w1ФΟ → УHД4 → ПμZ8 → ЗzΚG → ρ9МW → ГΘΒK → ι5Рe → ЛrΣC → ωPφO → αΥpm → cTςλ → ΝvΞy
876,248×(max) 33 nodesULАσ → εΜxi → kDИγ → υfζS → ΡnΧu → YLАο → εΔΖi → k1Фγ → Уfζ4 → ПnΧ8 → ЗXξG → ρΔΖW → Ι1ФΓ → У5Р4 → ПКB8 → ЗψNG → ρΩlW → ΙbκΓ → w5РΟ → ЛHДC → ωμZO → αzΚm → c9Мλ → ГvΞK → ιHДe → νrΣa → ΑPφΛ → Φ9Мq → ГTςK → ιΜxe → sDИΤ → υPφS → ΦΠtq
875,954×(max) 33 nodesA5РН → ЛВJC → ωθdO → αrΣm → cPφλ → ΦvΞq → UHДσ → νΜxa → ΑDИΛ → υ9МS → ГΠtK → ιLАe → εrΣi → kPφγ → Φfζq → oTςΨ → ΝXξy → ΕDИΗ → υ1ФS → УΠt4 → ПLА8 → ЗδhG → ρjβW → ΙfζΓ → o5РΨ → ЛXξC → ωΔΖO → α1Фm → Уbκ4 → ПvΞ8 → ЗHДG → ρμZW → ΙzΚΓ
875,578×(max) 33 nodesM5РБ → ЛδhC → ωjβO → αfζm → obκΨ → wXξΟ → ΕHДΗ → ν1Фa → УzΚ4 → П9М8 → ЗВJG → ρθdW → ΙrΣΓ → Q5Рχ → ЛΥpC → ωTςO → αΜxm → cDИλ → υvΞS → ΡHДu → νLАa → εzΚi → k9Мγ → ГfζK → ιnΧe → sXξΤ → ΕPφΗ → Φ1Фq → УTς4 → ПΜx8 → ЗDИG → υπVS → ΡΘΒu
875,568×(max) 33 nodesUDИσ → υΜxS → ΡDИu → υLАS → εΠti → kLАγ → εfζi → ojβΨ → gXξη → ΕnΧΗ → Y1Фο → УΔΖ4 → П1Ф8 → УЖF4 → ПπV8 → ЗΘΒG → ρ5РW → ЛΘΒC → ω5РO → ЛΩlC → ωbκO → αvΞm → cHДλ → νvΞa → ΑHДΛ → ν9Мa → ГzΚK → ι9Мe → ГrΣK → ιPφe → ΦrΣq → UPφσ → ΦΜxq
874,874×(max) 33 nodesMHДБ → νδha → ΑjβΛ → g9Мη → ГnΧK → ιXξe → ΕrΣΗ → Q1Фχ → УΥp4 → ПTς8 → ЗΜxG → ρDИW → υΘΒS → Ρ5Рu → ЛLАC → ωδhO → αjβm → gbκη → wnΧΟ → YHДο → νΔΖa → Α1ФΛ → У9М4 → ПВJ8 → ЗθdG → ρrΣW → ΙPφΓ → Φ5Рq → ЛTςC → ωΜxO → αDИm → υbκS → ΡvΞu
874,592×(max) 33 nodesA1ФН → УВJ4 → Пθd8 → ЗrΣG → ρPφW → ΦΘΒq → U5Рσ → ЛΜxC → ωDИO → υΩlS → Ρbκu → wLАΟ → εHДi → νjβa → ΑfζΛ → o9МΨ → ГXξK → ιΔΖe → s1ФΤ → УPφ4 → ПΥp8 → ЗTςG → ρΜxW → ΙDИΓ → υ5РS → ЛΠtC → ωLАO → εΩli → kbκγ → wfζΟ → oHДΨ → νXξa → ΕzΚΗ
874,576×(max) 33 nodesM1ФБ → Уδh4 → Пjβ8 → ЗfζG → ρnΧW → ΙXξΓ → Ε5РΗ → Л1ФC → УψN4 → ПΩl8 → ЗbκG → ρvΞW → ΙHДΓ → ν5Рa → ЛzΚC → ω9МO → ГΩlK → ιbκe → wrΣΟ → QHДχ → νΥpa → ΑTςΛ → Ν9Мy → ГDИK → υθdS → ΡrΣu → QLАχ → εΥpi → kTςγ → Νfζy → oDИΨ → υXξS → ΡΔΖu
872,568×(max) 33 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 cycles387,592,590×(max) 4 nodesδhЦδj → εhЦδi → εjЦβi → δiЦγj
18,088×2 nodesΖΔЦΖΖ → ΖЦЦЦΕ
613 cycles5,445,293,863×(max) 393 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
2,126,255,995×45 nodesqH9МЕΦ → ГξTςYK → ιΝΓΗxe → sF3ТЗΤ → ПςPφU8 → ЗΦΛypG → ρVBКρW → ωΚΘΒΑO → α95РНm → ЛДbκIC → ωμvΞaO → αzHДΛm → νcAЛκa → БΑuΟΚM → εK8НВi → ЕθjβeI → νrfζΤa → ΑoQυΧΛ → ΤX9Мοs → ГΖPφΕK → ιΦ0Хpe → ХsUρΣ2 → УΛOχz4 → ПΨAЛn8 → ЗБYνLG → ρζΒΘgW → Ιn5РΨΓ → ЛZ5РνC → ЛωΑΙNC → ωβ7ОkO → ЗαeηlG → ρqcιΥW → ΙuSσΠΓ → ΟL5РБw → ЛζHДgC → ωνmΨZO → αΒZμΙm → Αc6ПκΛ → Йv9МΟE → ГυIГRK → λιΡsdc → wtNψΡΟ → αNHДωm → νβbκka → ΑweηΞΛ
1,090,257,129×5 nodesΑUMωςΛ → γΜ9Мyk → ГgCЙζK → χιmΨdQ → ΦtZμΡq
223,481,064×22 nodeskdVπιγ → ΙtfζΡΓ → oN5РωΨ → ЛβXξkC → ωΕeηΖO → αq0ХΥm → ХcSσκ2 → УΟuΟv4 → ПKIГВ8 → ЗληebG → ρxpΥΝW → ΙUEЗςΓ → σΜ5РyU → ЛΝCЙxC → ωχEЗPO → σαΦolU → ΝdVπιy → ΙtDИΡΓ → υN5РωS → ЛβΠtkC → ωfLАηO → εαoΦli
64,870,116×18 nodesmcSσκα → ΟvbκΟw → wJHДГΟ → νκHДca → νΑuΟΚa → ΑK8НВΛ → Еθ9МeI → ГνqΤZK → ιΒRτΙe → Ρs6ПΣu → ЙPLАχE → υεΦohS → ΡlVπαu → ΙdLАιΓ → εt5РΡi → ЛkMωβC → ωγeηjO → αqgεΥm
25,318,536×4 nodesεa8Нμi → ЕzjβΛI → νgAЛζa → БΑmΨΚM
2,300,655×12 nodesεγ0Хji → Хkgεβ2 → УmeηΩ4 → ПqaλΥ8 → ЗySσΜG → ρΟCЙvW → χΙIГΒQ → λΦ6Пpc → ЙwUρΞE → υΛGЕzS → οΡAЛtY → БΕMωΖM
610,560×4 nodesηα2Уlg → СocιΧ6 → ЛuWοΠC → ωΗKБΔO
476,400×3 nodesιΨ4Сne → НsYνΣA → ГΓOχΘK
336,960×2 nodesνΤ8Нra → ЕΑQυΚI
268,110×2 nodesνi8Нδa → ЕΑiγΚI
176,400×(fixed) 1 node σΝEЗxU
4,556×(fixed) 1 node ΖΕЦЦΕΖ
7+---Not showing digit sets 7+ due to verbosity.