Base 111: 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 3 nodesFκ → ΣV → lΒ
31 cycle 2 nodessωu → tωt
447 cycles36 nodesJ6ςη → μΛbE → ΧYΞS → teΘu → T0ψΦ → ψqv2 → φ4τ4 → ςο98 → κεJG → ΣΙdW → lUΣΓ → nGθΑ → ΠCμY → ΩgΖQ → xOΩq → z6ςo → μAξE → δΦRM → Ζsti → N0ψγ → ψΓj2 → φIζ4 → ςΛb8 → κYΞG → ΣeΘW → lSΥΓ → rGθw → Π4τY → πgΖA → ζOΩK → Κyne → VAξΤ → δmzM → ΖCμi → ΩMβQ → Δwpk
51 cycle (fixed) 1 node ΝaωΜb
64 cycles85 nodesND9ομγ → ζΨΓjQK → ΚwIζqe → ΜV5σΣc → ξmYΞΑC → βfDλΘO → ΧΒRΦlS → usFιut → Σ20ψχW → ψυkΒ42 → φρGθ84 → ςιΟXG8 → κΡgΖWG → ΣkOΩΓW → zlHηΒo → ΞGAξιa → δΡcΚWM → ΖkWΠΓi → jNHηβΕ → ΞΓKδka → ΘdHηΚg → ΞWQΧΡa → vkcΚΓs → XI2φηΡ → τΝiΔa6 → ξcKδΛC → βΘXΟfO → ΒhRΦΖm → tOEκαu → ΥΑ0ψmU → ψpDλx2 → φΧ7ρR4 → ςκtsF8 → κΤ0ψUG → ψΣnyV2 → φmAξΑ4 → ςδDλL8 → κΧΖgRG → ΣuOΩsW → zl1χΒo → φGAξι4 → ςδΠWL8 → κΗiΔgG → ΣQKδΨW → ΘwkΒqg → RH5σθΨ → ξΟurYC → βg2φΗO → τΒPΨl6 → ξxFιpC → βΣ7ρVO → κΒlΑlG → ΣGEκιW → ΥΡkΒWU → pkGθΓy → ΠI8πηY → θΝgΖaI → ΞcOΩΛa → zdXΟΚo → hWAξΡΗ → δkOΩΓM → ΖzHηni → ΞNBνβa → βΓcΚkO → ΒXHηΠm → ΞiEκΕa → ΥdLγΚU → ΖpVΡxi → lN7ρβΓ → κΓGθkG → ΣΠHηXW → ΞlhΕΒa → dNFιβΛ → ΣΓWΠkW → ljHηΔΓ → ΞKGθεa → ΠΙcΚeY → hXTΤΠΗ → piOΩΕy → zM8πγo → θΕAξiI → δΞLγZM → ΗΕdΙih → VPLγΩΤ → Ζymzoi