Base 94: Cycles Sequences: Maximum Length Cycle Count

Blog: The First Pixel: Kaprekar's Constant 6174

Radix Character Encoding
0123456789ABCDEF
GHIJKLMNOPQRSTUV
WXYZabcdefghijkl
mnopqrstuvwxyzΑΒ
ΓΔΕΖΗΘΙΚΛΜΝΞΟΠΡΣ
ΤΥΦΧΨΩαβγδεζηθικ

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 nodes0θ → η1 → ε3 → α7 → ΡF → ΑV → UΒ → Wz → SΔ → av → KΜ → qf → AΧ → ΛL → oh → 6β → ΤD → ΕR → ct → GΠ → yX → QΖ → er → CΥ → ΗP → gp → 8Ω → ΟH → wZ → MΚ → mj → 2ζ → γ5 → ΦB → ΙN → kl
31 cycle (fixed) 1 node kθl
411 cycles23 nodesA5βΨ → ΦΜJC → ΙrdO → kDΣm → Ε1ζS → εbt4 → αHΞ8 → ΡvZG → ΑLΚW → oTΒi → Y5βy → ΦPΖC → ΙfpO → k9Χm → Ν1ζK → εrd4 → αDΣ8 → ΡΔRG → ΑbtW → UHΞΓ → wXxa → QLΚΗ → ofpi
53 cycles4 nodesΑUθΑW → ΒTθΒV → ΓVθzU → ΒWθyV
63 cycles53 nodesWTFΠΓΑ → ΑZTΒwW → YUMΙΒy → mXPΖyk → gR1ζΕq → εd9Χs4 → αΝEΡJ8 → ΡΓscTG → ΑZFΠwW → ΑUMΙΒW → mXTΒyk → YR1ζΕy → εdPΖs4 → αgEΡp8 → ΡΓ8ΨTG → ΟΑYwVI → wVNΘΑa → kVLΚΑm → oV1ζΑi → εV5βΑ4 → αΦUΑB8 → ΡΚVzMG → ΑnTΒiW → YU4γΒy → ΨXPΖyA → ΝgQΕpK → se8Ψre → ΟECΤΣI → ΗΔvZSQ → gbLΚuq → oJ9ΧΝi → Νt5βcK → ΦsGΟdC → ΙyEΡXO → ΓkQΕlU → eY0ηxs → ηPDΣΗ2 → εΕgoR4 → αd7Ωs8 → ΣΠEΡGF → ΔΒyWUT → aXRΔyw → cRLΚΕu → odHΞsi → wF5βΡa → ΦΒLΚUC → ΙoWyhO → kS6αΔm → Τb1ζuE → εΕIΝR4 → αucsb8 → ΡJFΠΝG → ΒzscWV
71 cycle 4 nodesΙkLθΚlO → ΛlNθΘkM → ΚnMθΙiN → ΚmPθΖjN