Base 65: 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--
24 cycles5 nodes9t → jJ → Pd → Dp → bR
31 cycle 2 nodesVΓX → WΓW
486 cycles6 nodesV0ΒY → Β2z2 → zw54 → vqB8 → neNG → XGlW
51 cycle 4 nodeshKΓhM → iKΓhL → iMΓfL → hLΓgM
66 cycles21 nodesnL1ΑhG → zXLgV4 → vL1Αh8 → znLgF4 → vYKhU8 → nN3yfG → vXHkV8 → nT1ΑZG → zX5wV4 → vr1ΑB8 → znfMF4 → vYIjU8 → nR3ybG → vX9sV8 → nj1ΑJG → zXPcV4 → vD1Αp8 → znbQF4 → vYArU8 → nh3yLG → vXLgV8
73 cycles4 nodeslVEΓnXI → oVFΓmXF → nZGΓlTG → mXHΓkVH
82 cycles19 nodesXI84xukW → tmS0ΒaGA → ΒjW7uWJ2 → znPΓΓcF4 → ynaArSF5 → thY7uULA → njM3ygJG → vXQJicV8 → nPC1ΑqdG → zeXDoVO4 → vbG1ΑmR8 → znW9sWF4 → vjXΓΓUJ8 → ujRBqbJ9 → lfQ9scNI → jTIBqkZK → fSP5wdaO → rHE7uolC → nfaTYSNG