Base 110: Cycles Sequences: All Cycle Counts

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 # Full Cycles
(excluding zero)
Frequency Cycle
Length
Full Cycles
(excluding zero)
(bold = exactly one cycle [excluding zero])
10 cycles---
23 cycles3,924×(max) 36 nodes0ψ → χ1 → υ3 → ρ7 → ιF → ΡV → kΒ → Gθ → ΟX → gΖ → OΩ → yn → Aξ → γL → Εh → Mβ → Γj → Iζ → Λb → YΞ → eΘ → SΥ → qv → 4τ → ο9 → εJ → Ιd → UΣ → mz → Cμ → ΨP → wp → 6ς → λD → ΦR → st
1,962×18 nodes2φ → σ5 → νB → αN → Αl → Eκ → ΤT → ox → 8π → ηH → ΝZ → cΚ → WΠ → iΔ → Kδ → Ηf → QΧ → ur
109×(fixed) 1 node 
31 cycle 227,810×(fixed) (max) 1 node sψt
421 cycles380,376×(max) 20 nodescXΞΛ → gXΞΗ → gPΧΗ → wPΧq → w5ςq → ν5ςC → νΩNC → αzlO → ΑDκm → ΦDκS → ΦrtS → s1φu → υ1φ4 → υπ74 → ρθF8 → ιΠVG → ΡjΒW → kHζΓ → ΝHζa → ΝbΚa
379,401×(max) 20 nodesIDκη → ΦΜZS → sbΚu → Y1φΟ → υfΖ4 → ρPΧ8 → ιvpG → Ρ5ςW → νjΒC → αHζO → Νzla → cDκΛ → ΦXΞS → sfΖu → Q1φΨ → υvp4 → ρ5ς8 → νθFC → αΠVO → ΑjΒm
377,799×(max) 20 nodes61φσ → υμB4 → ρΩN8 → ιzlG → ΡDκW → ΦjΒS → sHζu → Ν1φa → υbΚ4 → ρXΞ8 → ιfΖG → ΡPΧW → wjΒq → I5ςη → νΜZC → αbΚO → ΑXΞm → gDκΗ → ΦPΧS → wrtq
375,620×(max) 20 nodesE1φλ → υΥR4 → ρrt8 → ι1φG → υΠV4 → ρjΒ8 → ιHζG → ΡΜZW → kbΚΓ → YHζΟ → ΝfΖa → cPΧΛ → wXΞq → g5ςΗ → νPΧC → αvpO → Α5ςm → νDκC → αΥRO → Αrtm
373,758×(max) 20 nodesA1φο → υδJ4 → ρΘd8 → ιTΣG → ΡnxW → k9ξΓ → εHζK → ΝΘda → cTΣΛ → oXΞy → g9ξΗ → εPΧK → Ιvpe → U5ςΤ → νnxC → α9ξO → εzlK → ΙDκe → ΦTΣS → snxu
373,602×(max) 20 nodesE9ξλ → εΥRK → Ιrte → U1φΤ → υnx4 → ρ9ξ8 → ιδJG → ΡΘdW → kTΣΓ → oHζy → Ν9ξa → εbΚK → ΙXΞe → gTΣΗ → oPΧy → w9ξq → ε5ςK → νΘdC → αTΣO → Αnxm
372,658×(max) 20 nodesI9ξη → εΜZK → ΙbΚe → YTΣΟ → ofΖy → Q9ξΨ → εvpK → Ι5ςe → νTΣC → αnxO → Α9ξm → εDκK → ΦΘdS → sTΣu → o1φy → υ9ξ4 → ρδJ8 → ιΘdG → ΡTΣW → ojΒy
372,428×(max) 20 nodesA5ςο → νδJC → αΘdO → ΑTΣm → oDκy → Φ9ξS → εrtK → Ι1φe → υTΣ4 → ρnx8 → ι9ξG → εΠVK → ΙjΒe → UHζΤ → Νnxa → c9ξΛ → εXΞK → ΙfΖe → UPΧΤ → wnxq
372,382×(max) 20 nodesM5ςγ → νΔhC → αLβO → Εzli → MDκγ → ΦΔhS → sLβu → Ε1φi → υLβ4 → ρΔh8 → ιLβG → ΡΔhW → kLβΓ → ΕHζi → ΝLβa → ΕbΚi → YLβΟ → ΕfΖi → QLβΨ → Εvpi
362,689×(max) 20 nodesQHζΨ → Νvpa → c5ςΛ → νXΞC → αfΖO → ΑPΧm → wDκq → Φ5ςS → νrtC → α1φO → υzl4 → ρDκ8 → ιΥRG → ΡrtW → k1φΓ → υHζ4 → ρΜZ8 → ιbΚG → ΡXΞW → kfΖΓ
360,591×(max) 20 nodesUDκΤ → ΦnxS → s9ξu → ε1φK → υΘd4 → ρTΣ8 → ιnxG → Ρ9ξW → εjΒK → ΙHζe → ΝTΣa → obΚy → Y9ξΟ → εfΖK → ΙPΧe → wTΣq → o5ςy → ν9ξC → εΩNK → Ιzle
358,657×(max) 20 nodesE5ςλ → νΥRC → αrtO → Α1φm → υDκ4 → ρΥR8 → ιrtG → Ρ1φW → υjΒ4 → ρHζ8 → ιΜZG → ΡbΚW → kXΞΓ → gHζΗ → ΝPΧa → wbΚq → Y5ςΟ → νfΖC → αPΧO → Αvpm
358,147×(max) 20 nodesYDκΟ → ΦfΖS → sPΧu → w1φq → υ5ς4 → ρμB8 → ιΩNG → ΡzlW → kDκΓ → ΦHζS → Νrta → c1φΛ → υXΞ4 → ρfΖ8 → ιPΧG → ΡvpW → k5ςΓ → νHζC → αΜZO → ΑbΚm
357,427×(max) 20 nodesM1φγ → υΔh4 → ρLβ8 → ιΔhG → ΡLβW → ΕjΒi → MHζγ → ΝΔha → cLβΛ → ΕXΞi → gLβΗ → ΕPΧi → wLβq → Ε5ςi → νLβC → αΔhO → ΑLβm → ΕDκi → ΦLβS → Εrti
357,147×(max) 20 nodesQ5ςΨ → νvpC → α5ςO → νzlC → αDκO → ΦzlS → sDκu → Φ1φS → υrt4 → ρ1φ8 → υθF4 → ρΠV8 → ιjΒG → ΡHζW → ΝjΒa → cHζΛ → ΝXΞa → gbΚΗ → YPΧΟ → wfΖq
356,507×(max) 20 nodesI1φη → υΜZ4 → ρbΚ8 → ιXΞG → ΡfΖW → kPΧΓ → wHζq → Ν5ςa → νbΚC → αXΞO → ΑfΖm → QDκΨ → ΦvpS → s5ςu → ν1φC → υΩN4 → ρzl8 → ιDκG → ΦΠVS → sjΒu
188,007×10 nodesM9ξγ → εΔhK → ΙLβe → ΕTΣi → oLβy → Ε9ξi → εLβK → ΙΔhe → ULβΤ → Εnxi
173,000×10 nodesg1φΗ → υPΧ4 → ρvp8 → ι5ςG → νΠVC → αjΒO → ΑHζm → ΝDκa → ΦbΚS → sXΞu
85,450×5 nodeso9ξy → ε9ξK → εΘdK → ΙTΣe → oTΣy
85,450×5 nodesU9ξΤ → εnxK → Ι9ξe → εTΣK → Ιnxe
17,534×(fixed) 1 node ΕLβi
52 cycles146,790,954×(max) 4 nodesΜZψΜb → ΝZψΜa → ΝbψΚa → ΜaψΛb
12,208×2 nodestrψtt → tψψψs
67 cycles1,319,461,132×148 nodesMA8οξγ → ηδΔhKI → ΝΘLβea → ΕcSΤΚi → qXLβΟw → Εh5ςΕi → νNLβαC → αΕΑkhO → ΑNFθαm → ΡΒDκkW → ΦkGηΒS → ΟsGηtY → Οg0χΖY → χgOΨΖ2 → υyOΨn4 → ρyAνn8 → ιγAνLG → γΡΕgVM → ΕlNΩΑi → ΑMEιβm → ΤΔDκiU → ΦoKγxS → Ηs8οtg → ηQ0χΧI → χΝuqZ2 → υd3τΙ4 → ςπUΡ87 → λθlzGE → ΦΠDκWS → ΦsiΓtS → sK0χδu → χΘ1φe2 → φτSΤ43 → σπpv86 → νθ5ςGC → ναΟWNC → αΒhΔkO → ΑMGηβm → ΟΔDκiY → ΦgKγΖS → ΗsOΨtg → yQ0χΧo → χv9ξq2 → υε4σJ4 → ροΙc98 → ιζVΠIG → ΡΜjΒaW → kbHζΛΓ → ΝZHζΝa → ΝdbΚΙa → cYUΡΞΛ → mfXΞΗΑ → gRDκΦΗ → ΦtPΧsS → ws0χtq → χ60χς2 → χυλC32 → υςΧP64 → ρμvpC8 → ιΩ5ςOG → νΡymVC → αlBμΑO → αΑEιlO → ΤΑEιlU → ΤoEιxU → Τo8οxU → ηo8οxI → ηΝ8οZI → ηΝcΙZI → ΝdVΠΙa → kcUΡΚΓ → mXHζΟΑ → ΝhDκΕa → ΦcMαΚS → ΓsWΟtk → iI0χζΕ → χΜLβa2 → υΕaΛh4 → ρaMαΜ8 → ιΓaΛjG → ΡaIεΜW → ΛkaΛΒc → aYGηΞΝ → ΟfbΚΗY → gYQΦΞΗ → ufPΧΗs → wR1φΦq → υt5ςs4 → ρν0χB8 → χιαMF2 → υΣΒjU4 → ρnHζy8 → ιΝAνZG → γΡcΙVM → ΕlVΠΑi → kMEιβΓ → ΤΔHζiU → ΝoKγxa → Ηc8οΚg → ηXPΧΟI → ΝwgΕpa → cO6ρΩΛ → λzXΞmE → ΦgCλΖS → ΨsOΨtQ → yw0χpo → χA6ρξ2 → υλγKD4 → ρΧΖfQ8 → ιvPΧqG → Ρw4σpW → οk6ρΒA → λεGηJE → ΦΟΙcXS → shVΠΕu → kN1φαΓ → υΒHζk4 → ρΝGηZ8 → ιΟcΙXG → ΡhVΠΕW → ljMαΓΒ → ΓJFθεk → ΡΚHζcW → ΝkWΟΒa → icGηΚΕ → ΟXLβΟY → ΕhfΖΕi → QNLβαΨ → ΕΒvpki → MH5ςηγ → νΞΔhYC → αfLβΗO → ΕΑQΦli → uMEιβs → ΤΔ1φiU → υoKγx4 → ρΗ8οf8 → ιηQΦHG → ΡΞtrYW → kf1φΗΓ → υRHζΦ4 → ρΝssZ8 → ιcψψΙG → θΚNΩcH → ΟΑWΟlY → igEιΖΕ → ΤPLβΨU → Εxnxoi
557,654,792×(max) 171 nodesUNFθαΤ → ΡΒnxkW → kH9ξηΓ → εΞHζYK → ΝΙeΗda → cVRΥΡΛ → slXΞΑu → gF1φιΗ → υΣPΧU4 → ρwmyp8 → ιC6ρμG → λΩΠVOE → ΦzjΒmS → sICλζu → ΨΜ1φaQ → υwaΛp4 → ρa6ρΜ8 → λιaΛFE → ΦΣZΜUS → snbΚyu → YB1φνΟ → υβfΖM4 → ρΔPΧi8 → ιwKγpG → ΡΗ6ρfW → λkQΦΒE → ΦuGηrS → Οs2υtY → σg0χΖ6 → χνOΨB2 → υβxnM4 → ρΔ9ξi8 → ιεKγJG → ΡΚΖfcW → kXPΧΟΓ → whHζΕq → ΝN5ςαa → νΒbΚkC → αYGηΞO → ΟΑeΗlY → gSEιΥΗ → ΤrPΧuU → wo2υxq → σ95ςο6 → ξμεICB → γΩΚbOM → ΕzXΞmi → gMCλβΗ → ΨΔPΧiQ → xvKγqp → Η84σπg → οθPΧGA → εΠvpWK → Ιj5ςΓe → νUIεΣC → αΛmybO → ΑZBμΝm → αdDκΙO → ΦΑUΡlS → smEιzu → ΤD1φλU → υΧnxQ4 → ρv9ξq8 → ιε4σJG → οΡΙcVA → εlVΠΑK → ΙkEιΒe → ΤUGηΣU → ΟomyxY → gC8ομΗ → ηΩPΧOI → Νzvpma → cD5ςλΛ → νΧXΞQC → αvfΖqO → ΑQ4σΧm → οvDκqA → εΦ4σRK → οΙssdA → εUψψΡK → δΣBμUL → αΗmyfO → ΑRBμΦm → αtDκsO → ΦΑ0χlS → χsEιt2 → υΤ0χT4 → χρow72 → υκ7πE4 → ριΤSF8 → ιΣpvUG → Ρn5ςyW → νkAνΒC → γαGηNM → ΟΕΑkhY → gNFθαΗ → ΡΒPΧkW → wkGηΒq → ΟH5ςηY → νΞfΖYC → αfPΧΗO → ΑwQΦpm → uE6ρκs → λΥ1φSE → υΦquR4 → ρt3τs8 → ρι0χF8 → χιΡUF2 → υΣlzU4 → ρnDκy8 → ιΦAνRG → γΡssVM → ΕkψψΑi → ΔΒ3τkj → ρKGηδ8 → ιΟΗeXG → ΡhRΥΕW → skMαΒu → ΓH1φηk → υΞHζY4 → ρΝeΗZ8 → ιdRΥΙG → ΡsUΡtW → mk0χΒΑ → χHDκη2 → υΦΝYR4 → ρtdΘs8 → ιU0χΣG → χΡmyV2 → υlBμΑ4 → ραEιN8 → ιΤΑkTG → ΡpFθwW → Ρk6ρΒW → λkGηΒE → ΦΟGηXS → ΟsgΕtY → gO0χΩΗ → χzPΧm2 → υwCλp4 → ρΨ6ρP8 → λιwoFE → ΦΣ7πUS → ιsmytG → ΡC0χμW → χΩjΒO2 → υzHζm4 → ρΝCλZ8 → ιΨcΙPG → ΡxVΠoW → lj8οΓΒ → ηJFθεI → ΡΝΙcZW → kdVΠΙΓ → kVHζΡΓ → ΝlHζΑa → ΝcEιΚa → ΤcWΟΚU → oiWΟΔy → iL9ξγΕ → εΖLβgK → ΙΕOΨhe → yUMαΣo → Γn9ξyk → εIAνζK → γΜΘdaM → ΕbTΣΛi → oZLβΝy → Εd9ξΙi → εVLβΡK → ΙΕkΑhe
429,752,327×71 nodesMKEιδγ → ΤΘΔheU → oTLβΤy → Εp9ξwi → εM6ρβK → λΙΓidE → ΦVJδΡS → ΙskΑte → UG0χθΤ → χΠnxW2 → υj9ξΓ4 → ρεIεJ8 → ιΛΙcbG → ΡZVΠΝW → ljcΙΓΒ → WJFθεΡ → ΡΚjΒcW → kXHζΟΓ → ΝhHζΕa → ΝcMαΚa → ΓcWΟΚk → iXHζΟΕ → ΝhLβΕa → ΕcMαΚi → ΓXLβΟk → ΕhHζΕi → ΝNLβαa → ΕΒbΚki → YMGηβΟ → ΟΔfΖiY → gQKγΧΗ → ΗvPΧqg → wQ4σΧq → οv5ςqA → νε4σJC → οαΙcNA → εΒVΠkK → ΙkGηΒe → ΟUGηΣY → ΟnfΖyY → gQAνΧΗ → γvPΧqM → Εw4σpi → οM6ρβA → λεΓiJE → ΦΚJδcS → ΙsWΟte → iU0χΣΕ → χnLβy2 → υΕAνh4 → ργMαL8 → ιΖΒjgG → ΡPHζΨW → ΝxjΒoa → cI8οζΛ → ηΜXΞaI → ΝgaΛΖa → caOΨΜΛ → ybXΞΛo → gZ9ξΝΗ → εdPΧΙK → ΙwUΡpe → mU6ρΣΑ → λnDκyE → ΧΥAνSR → γuqurM → Ε42υτi → σπLβ86 → νθΔhGC → αΠLβWO → ΕΑiΓli
347,428,550×75 nodesSLDκγΦ → ΦΖrtgS → sP1φΨu → υx1φo4 → υρ8ο74 → ρκζHE8 → ιΥΜZSG → ΡrbΚuW → kY2υΞΓ → σfHζΗ6 → νΝQΦZC → αucΙrO → ΑW2υΠm → σjDκΓ6 → νΦIεRC → αΛssbO → ΑYψψΝm → ΞzBμmZ → αeCλΘO → ΨΑSΤlQ → wqEιvq → Τ64σςU → ομnxCA → εΩ9ξOK → εΙymdK → ΙVBμΡe → αlTΣΑO → ΑoEιxm → ΤE8οκU → ηΥnxSI → Νr9ξua → εc2υΚK → σΙWΟd6 → νiUΡΔC → αmKγzO → ΗΑCλlg → ΨQEιΧQ → ΤwuqpU → o73τρy → ρκ9ξE8 → ιεΤSJG → ΡΚpvcW → kX5ςΟΓ → νhHζΕC → αΝMαZO → ΓΑcΙlk → WIEιζΡ → ΤΜjΒaU → obHζΛy → ΝZ9ξΝa → εdbΚΙK → ΙYUΡΞe → mfTΣΗΑ → oRDκΦy → Φt9ξsS → εs0χtK → χΙ0χd2 → χυUΡ32 → υςlz64 → ρμDκC8 → ιΩΥROG → ΡzrtmW → kD1φλΓ → υΧHζQ4 → ρΝuqZ8 → ιd3τΙG → ρΡUΡV8 → ιmkΑzG → ΡGCλθW → ΨΠjΒWQ → wjHζΓq → ΝJ5ςεa → νΚbΚcC → αYWΟΞO → ΑieΗΔm
157,496,374×93 nodesIA4σξη → οδΜZKA → εΘbΚeK → ΙYSΤΞe → qfTΣΗw → oR5ςΦy → νt9ξsC → εα0χNK → χΙΑkd2 → υVFθΡ4 → ρΡkΑV8 → ιlFθΑG → ΣΠEιWV → ΤmiΓzU → oKCλδy → ΨΘ9ξeQ → εwSΤpK → Ιq6ρve → λU4σΣE → οΦmyRA → εtBμsK → αΙ0χdO → χΑUΡl2 → υmEιz4 → ρΤCλT8 → ιΨowPG → Ρx7πoW → ιk8οΒG → ηΡGηVI → ΟΝkΑZY → gdFθΙΗ → ΡVPΧΡW → wljΒΑq → IF5ςιη → νΣΜZUC → αnbΚyO → ΑYAνΞm → γfDκΗM → ΦΕQΦhS → usMαts → Γ20χφk → χτHζ42 → υπΜZ84 → ρθbΚG8 → ιΠXΞWG → ΡjfΖΓW → kQIεΧΓ → ΛvHζqc → ΝY4σΞa → οfbΚΗA → εYQΦΞK → ΙueΗre → US2υΥΤ → σrnxu6 → νA2υξC → σδΩNK6 → νΘzleC → αTDκΤO → ΦΑowlS → sF7πιu → ιΣ1φUG → υΡmyV4 → ρlBμΑ8 → ιαEιNG → ΤΡΑkVU → olFθΑy → ΡF9ξιW → εΣjΒUK → ΙnHζye → ΝUAνΣa → γnbΚyM → ΕYAνΞi → γfLβΗM → ΖΔQΦih → uOKγΩs → Ηz1φmg → υQCλΧ4 → ρΨuqP8 → ιx3τoG → ρΡ8οV8 → ιηkΑHG → ΡΞFθYW → ΡkeΗΒW → kSGηΥΓ → ΟrHζuY → Νg2υΖa → σcOΨΚ6 → νyWΟnC → αiAνΔO → γΑKγlM → ΗΕEιhg → ΤQMαΧU → Γvnxqk
1,933,015×18 nodesΝΛ0χba → χcYΝΚ2 → υeWΟΘ4 → ρiSΤΔ8 → ιqKγvG → ΡΗ4σfW → οkQΦΒA → εuGηrK → ΟΙ2υdY → σgUΡΖ6 → νmOΨzC → αyCλnO → ΨΑAνlQ → γwEιpM → ΤΕ6ρhU → λoMαxE → ΦΓ8οjS → ηsIεtI
3,080×(fixed) 1 node tsψψst
7+---Not showing digit sets 7+ due to verbosity.