Base 74: Cycles Sequences: Maximum Length Cycle Count

Blog: The First Pixel: Kaprekar's Constant 6174

Radix Character Encoding
0123456789ABCDEF
GHIJKLMNOPQRSTUV
WXYZabcdefghijkl
mnopqrstuvwxyzΑΒ
ΓΔΕΖΗΘΙΚΛΜΝΞΟΠΡΣ

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--
25 cycles20 nodes0Μ → Λ1 → Ι3 → Ε7 → wF → gV → AΒ → qL → Uh → Cz → mP → Mp → Sj → Gv → eX → 6Ζ → yD → kR → It → ab
31 cycle (fixed) 1 node aΜb
49 cycles18 nodesE1Κy → ΙjR4 → ΕHt8 → wbZG → g1ΚW → Ι9Β4 → ΕrJ8 → wXdG → g5ΖW → Α9ΒC → snNK → YPle → M5Ζq → ΑThC → oDxO → kPlS → MHtq → cTha
52 cycles4 nodesnNΜnP → oNΜnO → oPΜlO → nOΜmP
65 cycles49 nodesA73ΘΕΓ → ΕxrJE8 → wjXdSG → gH5ΖuW → Αd9ΒYC → so4ΗNK → ΓYQkdA → sK4ΗrK → ΓYWedA → s84ΗΔK → ΓvXdGA → sf5ΖWK → ΑY8ΓdC → uo4ΗNI → ΓcQkZA → sK2ΙrK → ΗYWed6 → Α84ΗΔC → ΓvnNGA → sfPlWK → YM8Γpe → uT5ΖiI → ΑcEwZC → oi2ΙTO → ΗQEwl6 → ΑiKqTC → oWEwfO → iQ8ΓlU → uLDxqI → kcUgZS → IC2Ιzu → ΗnbZO6 → ΑP1ΚmC → ΙoMoN4 → ΕSQkj8 → wKGurG → geWeXW → A86ΕΔΓ → yvrJGE → kfXdWS → I95ΖΓu → ΑtbZIC → ob1ΚaO → ΙQ0Λl4 → ΛΕKq72 → ΙxVfE4 → Εj9ΒS8 → wsGuJG → geYcXW
71 cycle 4 nodestaGΜubJ → vbIΜsaH → udHΜtYI → ucKΜqZI