Base 85: 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 cycles7 nodesDΚ → vR → Tt → Px → Xp → HΖ → nZ
31 cycle 2 nodesfΨh → gΨg
4117 cycles8 nodesLAΜΓ → ΒgfM → f0Χi → Χ2Υ2 → ΥΡ54 → ΠΛB8 → ΘyNG → ralW
52 cycles4 nodesuRΨuT → vQΨvS → wSΨtR → vTΨsS
610 cycles49 nodesL60ΧΡΓ → ΧΛgfC2 → Υy0ΧO4 → ΧΠZm72 → ΥΙCΚE4 → ΠxtSP8 → ΘYQvoG → rVFΗrW → rMKΒΑW → heKΒig → h40ΧΤg → ΧΟ0Χ82 → ΧΥΖG32 → ΥΡoX64 → ΠΛGΖC8 → ΘyoXOG → raGΖmW → pLBΛΒY → zgGΖgO → paΨΨlY → om3ΤaZ → ΠFBΛΘ8 → ΘzrUNG → rcMzkW → dL7ΟΒk → Θg6ΠgG → ΚqΨΨVE → ΙrIΔVF → tlLΑbU → fP9Νxi → ΔY2ΥoK → ΣjFΗd6 → Μr5ΡVC → ΜzLΑNC → zfbkhO → b91ΦΞm → ΥΕAΜI4 → ΠΒlaL8 → ΘgAΜgG → ΒqΨΨVM → ΑrAΜVN → ΒdLΑjM → ge5Ρih → Μ40ΧΤC → ΧΟyN82 → ΥΗalG4 → ΠqAΜW8 → ΘΒJΓLG → rjfgdW
73 cycles4 nodesΑfJΨΓhN → ΔfKΨΒhK → ΓjLΨΑdL → ΒhMΨzfM