Base 86: 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 cycles28 nodes0Ω → Ψ1 → Φ3 → Ρ7 → ΙF → sV → MΒ → ej → 4Υ → Ο9 → ΕJ → kd → 6Σ → ΛD → wR → Ut → Oz → an → CΜ → yP → Yp → GΘ → qX → IΖ → mb → AΞ → ΓL → gh
31 cycle (fixed) 1 node gΩh
430 cycles7 nodesM1ΧΓ → Φfh4 → Ρ1Χ8 → ΦΘF4 → ΡrV8 → ΙLΒG → sfhW
52 cycles4 nodesvRΩvT → wRΩvS → wTΩtS → vSΩuT
67 cycles43 nodesSM0ΨΒw → ΨfTti2 → ΦQ2Φx4 → ΤΡWq76 → ΝΚJΔEC → ΑvjdSO → cT5Σum → ΝR9ΞwC → ΕΑUsNK → kdNzke → c75ΣΡm → ΝΚ9ΞEC → ΕΑuSNK → kdRvke → U75ΣΡu → ΝΚPxEC → ΑvXpSO → cTHΖum → oR9Ξwa → ΕVDΚsK → wkMΑdS → eU6Ρtk → ΛP5ΣyE → ΝwYoRC → ΑVFΘsO → scMΑlW → eM8ΟΒk → Ηf5ΣiI → Νo2ΦZC → ΤΑEΙN6 → ΝuckTC → ΑR7ΠwO → ΙcUslG → sO8ΟzW → ΗbLΒmI → ogAΝha → ΓE0ΨΚM → ΨvfhS2 → ΦT1Χu4 → ΦΡQw74 → ΡΚVrE8 → ΙvLΒSG → sgSuhW
71 cycle 4 nodesΓgJΩΔhM → ΕhLΩΒgK → ΔjKΩΓeL → ΔiNΩzfL