Base 93: 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--
21 cycle 23 nodes1ζ → δ3 → Ω7 → ΠF → zV → TΒ → Xx → PΖ → fp → 9Χ → ΜJ → rd → DΣ → ΔR → bt → HΞ → vZ → LΚ → nh → 5β → ΥB → ΘN → jl
31 cycle 2 nodesjηl → kηk
4117 cycles10 nodesN0ζΙ → ζkj2 → δ0ζ4 → ζΨ72 → δΟF4 → ΩyV8 → ΠSΒG → zYvW → TMΘΓ → lYvk
51 cycle (fixed) 1 node ΑUηzV
64 cycles59 nodesbWMΘyu → lSIΜΓk → ta0ζuc → ζKGΞΛ2 → δxpeX4 → ΩQAΥΕ8 → ΠΚdqLG → zoCΣgW → ΖT7ΨΒQ → ΠfXwpG → zP9ΦΖW → ΜgSΒoK → rZ7Ψve → ΠMCΣΙG → ΖzliVQ → fU2δΑq → βWAΥy6 → ΥΚRΓLC → ΘoatgO → jJ7ΨΜm → Πs2δcG → βzFΟV6 → ΥzTΑVC → ΘXTΑxO → jXPΕxm → fQ2δΕq → βeAΥq6 → ΥΚBΤLC → ΙΗngON → li6Ωmk → Σ40ζγE → ζΨΓR82 → δΟatG4 → ΩyIΜW8 → ΠtRΓbG → zbHΝtW → vTHΝΒa → vYKΚwa → pOKΚΗg → pi8Χmg → Ξ93γΧI → ΩΝuZI8 → ΠuKΚaG → zpJΛfW → rT9ΦΒe → ΜYCΣwK → ΖrNΗdQ → jfDΡpm → ΔA2δΦS → βΛatK6 → ΥqIΜeC → ΘtBΤbO → ΘjHΝlO → vj1εla → δL1εΚ4 → δΩng74 → ΩΡ6ΩE8 → ΣΠΒSFE → ΔΑYvUS
73 cycles4 nodesΗjLηΙlP → ΚjMηΘlM → ΙnNηΗhN → ΘlOηΖjO