Base 110: Cycles Sequences: Maximum Length Cycle Count

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)
Max Cycle
Length
Longest Full Cycles
(excluding zero)
(bold = exactly one cycle [excluding zero])
10 cycles--
23 cycles36 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
31 cycle (fixed) 1 node sψt
421 cycles20 nodesI1φη → υΜZ4 → ρbΚ8 → ιXΞG → ΡfΖW → kPΧΓ → wHζq → Ν5ςa → νbΚC → αXΞO → ΑfΖm → QDκΨ → ΦvpS → s5ςu → ν1φC → υΩN4 → ρzl8 → ιDκG → ΦΠVS → sjΒu
52 cycles4 nodesΜZψΜb → ΝZψΜa → ΝbψΚa → ΜaψΛb
67 cycles171 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