Base 69: 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--
23 cycles12 nodes1Ζ → Δ3 → z7 → rF → bV → 5Β → vB → jN → Ll → Ph → Hp → XZ
31 cycle 2 nodesXΗZ → YΗY
429 cycles22 nodesB4Βw → xkLA → nOhK → TIne → VAvc → l6zM → tOhE → fInS → VCtc → h6zQ → tGpE → fYXS → D0Ζu → ΖgP2 → ΔGp4 → zYX8 → r0ΖG → ΖaV2 → Δ4Β4 → zw98 → rmJG → bSdW
51 cycle (fixed) 1 node kMΗjN
63 cycles39 nodesF4ΗΗΒs → Γr8xF5 → xpbUHA → nY6zYK → tSΗΗdE → seFqSF → dbBuVU → j95ΑxO → voKlIC → jWQfaO → LF3Γrm → zcQfU8 → rF7yrG → rcaVUG → b84ΒyW → xq4ΒGA → xnZWJA → nU2ΔcK → ΒT7yd6 → vr9wFC → njbUNK → TM6zke → tOAviE → lfJmRM → TPDshe → fIAvoS → lWCtaM → hP3ΓhQ → zIGpo8 → rZVaXG → b51ΕΒW → Δw4ΒA4 → zxlK98 → roQfIG → bWEraW → d53ΓΒU → zw8xA8 → rplKHG → bYQfYW
73 cycles4 nodesoXFΗqZJ → rXGΗpZG → qbHΗoVH → pZIΗnXI
85 cycles7 nodesbUT7ydcW → rA84ΒywG → xqmaVKGA → naS4ΒeWK → xTC3ΓudA → zni9wOJ8 → rnUJmcJG