Base 102: 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 51 nodes0π → ο1 → ν3 → ι7 → αF → ΙV → cΒ → OΠ → qn → 2ξ → λ5 → εB → ΡN → sl → 6κ → γD → ΝR → kt → 8θ → ΨH → ΕZ → UΚ → ez → KΥ → yf → IΧ → Γb → QΞ → mr → 4μ → η9 → ΦJ → Αd → MΣ → uj → Aζ → ΤL → wh → Eβ → ΛT → gx → GΩ → ΗX → YΖ → WΘ → aΔ → SΜ → iv → Cδ → ΟP → op
31 cycle (fixed) 1 node oπp
444 cycles8 nodesQ1ξΟ → νnp4 → ι1ξ8 → νΩF4 → ιΘV8 → αbΒG → ΙPΞW → obΒq
52 cycles2 nodespnπpp → pπππo
64 cycles46 nodesUO8ηΠΛ → ΨrfxmI → ΕI4λΧa → ηΔTΚaA → ΦgSΛxK → ΑiGΨve → ΗMCγΣY → ΟvXΖiQ → oYCγΖq → ΟX1ξΗQ → νoYΕp4 → ιW0οΘ8 → οαaΓF2 → νΚRΜU4 → ιkeyt8 → αK8ηΥG → ΨΙyeVI → ΕdJΥΑa → ΑUMΡΚe → ufLΣyk → wJ9ζΦi → ΦΒDβcK → ΝΑOΟdS → qkMΡto → u91ξηk → νΧ9ζI4 → ιΦΓaJ8 → αΒRΜcG → ΙkOΟtW → qc8ηΒo → ΨP1ξΟI → νΕooZ4 → ιUππΙ8 → θΚNΠU9 → ΨseylI → ΕK6ιΥa → γzTΚeE → ΝgKΤxS → ykGΨtg → ΗI8ηΧY → ΨΔXΖaI → ΕYSΛΖa → iXTΚΗw → gZDβΕy → ΝVHΧΙS → ΕkcΑta