Base 106: 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--
21 cycle 53 nodes0τ → σ1 → ρ3 → ν7 → εF → ΝV → gΒ → KΩ → Γf → MΧ → yj → Eζ → ΟT → kx → Cθ → ΤP → sp → 2ς → ο5 → ιB → ΦN → wl → Aκ → ΨL → Αh → Iβ → Ηb → UΞ → iz → Gδ → ΛX → cΖ → SΠ → mv → 8μ → γH → ΙZ → YΚ → aΘ → WΜ → eΔ → OΥ → un → 6ξ → ηD → ΡR → ot → 4π → λ9 → αJ → Εd → QΣ → qr
31 cycle (fixed) 1 node qτr
413 cycles26 nodesE1ςη → ρΠR4 → νnt8 → ε5ξG → ιΜVC → ΦfΒO → wLΧm → Α9κi → αHβK → ΙΔda → YPΣΛ → sbΖq → U1ςΟ → ρjx4 → νDζ8 → εΠRG → ΝntW → g5ξΓ → ιLΧC → ΦzhO → wHβm → Ι9κa → αXΚK → ΕbΖe → UPΣΟ → sjxq
53 cycles4 nodesΙYτΙa → ΚXτΚZ → ΛZτΘY → ΚaτΗZ
66 cycles253 nodesGA6νκε → ηΩΜVKE → ΡΔfΒeS → oPLΧΤu → Αt5ξoi → ιI4οβC → λΦΗaNA → αxVΜkK → ΕgCηΒe → ΤQKΨΣQ → Γsqqpg → M2ττρΨ → ςΧHβM3 → οΙyiZ6 → ιZFδΙC → ΦΝYΙVO → whZΘΑm → YJ9καΛ → αΖbΖcK → ΕUSΟΞe → mjPΣyw → sF9κεq → αΞ1ςUK → ρΕiyd4 → νRFδΡ8 → εΝosVG → Νh3πΑW → νgIαΒ8 → εΗKΨbG → ΝΓUΝfW → igMΦΒΑ → yLHβΨk → ΙΒDζga → ΡYKΨΚS → ΓoaΗtg → WM4οΧΝ → λzfΒiA → αMGγΧK → ΛΕyidY → cRFδΡΗ → ΝpTΞsW → kg2ρΒy → οLDζΨ6 → ιΡΑgRC → ΦpJΩsO → Εw2ρle → οQAιΣ6 → ιΨqqLC → ΦΑττgO → ΥΒJΩgP → ΕuKΨne → ΓQ6νΣg → ηrLΧqE → ΡΑ0σhS → σoIαt2 → ρΗ4οb4 → νλUΝ98 → εβhzIG → ΝΘHβaW → ΙgWΛΒa → eYKΨΚΕ → ΓbPΣΗg → sVLΧΝq → Αh1ςΑi → ρJHβα4 → νΙΕcZ8 → εZRΠΙG → ΝoYΙtW → ga4οΘΓ → λXLΧΛA → αΑcΕhK → ΕSIαΠe → ΗnPΣuc → sU6νΞq → ηj1ςyE → ρΡEεR4 → νΟosT8 → εl3πwG → νΝAιV8 → εΨgΑLG → ΝΒJΩgW → ΕgKΨΒe → ΓQKΨΣg → ΓrLΧqg → ΑM0σΧi → σzHβi2 → ρΙGγZ4 → νΛYΙX8 → εdZΘΕG → ΝYQΡΚW → qgaΗΒs → WL1ςΨΝ → ρΒfΒg4 → νMKΨΧ8 → εΓyifG → ΝNFδΦW → ΝxfΒkW → gMCηΧΓ → ΤzLΧiQ → ΑsGγpi → ΛI2ρβY → οΘbΖa6 → ιXTΞΛC → ΦkcΕxO → wSCηΠm → Τn9κuQ → αs6νpK → ηΕ2ρdE → οΡQΡR6 → ιqosrC → Φ40σπO → σμvl82 → ρδ9κG4 → ναΛWJ8 → εΖdΔcG → ΝTPΣΟW → slfΒwq → MB1ςιΨ → ρΧzhM4 → νzHβi8 → εΙGγZG → ΝΛYΙXW → gdZΘΕΓ → YRLΧΡΛ → ΑpbΖsi → UI2ρβΟ → οΘjxa6 → ιXDζΛC → ΦΡcΕRO → wpRΠsm → oA2ρκu → οΩ5ξK6 → κθΓeCB → ΨΥNΥOM → Αwumli → IB7μιγ → εΧΘZMG → ΝzXΚiW → gcGγΖΓ → ΛTLΧΟY → ΑlbΖwi → UIAιβΟ → ΨΘjxaM → ΑXDζΛi → ΡdHβΕS → ΙoQΡta → qY4οΚs → λb1ςΗA → ραUΝJ4 → νΖhzc8 → εTHβΟG → ΝΙkwZW → gZBθΙΓ → ΦZLΧΙO → ΑwYΙli → aIAιβΙ → ΨΘXΚaM → ΑcWΛΖi → eTHβΟΕ → ΙlPΣwa → sYAιΚq → Ψb1ςΗM → ρΑUΝh4 → νiIαz8 → εΗGγbG → ΝΛUΝXW → igcΕΒΑ → SLHβΨΡ → ΙΒntga → YL5ξΨΛ → ιΒbΖgC → ΦUKΨΞO → Γwiylg → MGAιδΨ → ΨΜzhWM → ΑfHβΓi → ΙNHβΦa → ΙxXΚka → cYCηΚΗ → ΤbTΞΗQ → skUΝxq → iD1ςηΑ → ρΣHβQ4 → νΙqqZ8 → εYττΙG → δΚJΩYH → ΛΕaΗdY → cWQΡΜΗ → qfTΞΓs → kN1ςΦy → ρxDζk4 → νΡCηR8 → εΤosPG → Νt3πoW → νg4οΒ8 → λεKΨFA → αΞΒfUK → ΕjLΧye → ΑQEεΣi → ΟrHβqU → Ιk0σxa → σYCηΚ2 → ρΤaΗP4 → νtVΜo8 → εg4οΒG → λΝKΨVA → αΓgΑfK → ΕNJΩΦe → ΕxPΣke → sQCηΣq → Τr1ςqQ → ρs0σp4 → σν2ρ72 → ροεE54 → νκΞTA8 → εΩjxKG → ΝΔDζeW → ΡgOΤΒS → uoKΨto → Γ64οξg → λθLΧCA → αΥzhOK → ΕvHβme → ΙQ8λΣa → γrXΚqI → Ιc0σΖa → σYSΟΚ2 → ρmaΗv4 → νW8λΜ8 → εγeΓHG → ΝΚNΥYW → wgaΗΒm → WL9κΨΝ → αΒfΒgK → ΕMKΨΧe → ΓzPΣig → sMGγΧq → Λz1ςiY → ρcGγΖ4 → νΛSΟX8 → εmcΕvG → ΝS8λΠW → γnfΒuI → ΙM6νΧa → ηzXΚiE → ΡcGγΖS → ΛoSΟtY → mc4οΖw → λT9κΟA → βΩkwKJ → ΗΔBθec → ΦUOΤΞO → wuiynm