Base 73: 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--
21 cycle 18 nodes1Κ → Θ3 → Δ7 → vF → fV → 9Β → rJ → Xd → 5Ζ → zB → nN → Pl → Lp → Th → Dx → jR → Ht → bZ
31 cycle 2 nodesZΛb → aΛa
470 cycles9 nodesN8Βo → tQjI → bIra → Z0Κc → Κ2Θ2 → ΘΕ54 → ΔyB8 → vmNG → fOlW
52 cycles4 nodesmNΛmP → nMΛnO → oOΛlN → nPΛkO
62 cycles29 nodes973ΗΔΓ → ΔwsHE8 → viaZSG → fG0ΚuW → Κe8ΒW2 → Θt7ΓH4 → ΔvbYF8 → vg2ΘUG → ΖfByV6 → zn9ΑNC → rnPkNK → XQKpke → VK6Δqg → xWAzeE → pj7ΓRM → vTHshG → fbDwZW → j91ΙΒS → ΘsGtI4 → ΔdZaX8 → v60ΚΕG → ΚyeVC2 → Θm8ΒO4 → ΔtNmH8 → vcOlYG → fN3ΗnW → ΔQ8Βk8 → vtJqHG → fcWdYW
73 cycles4 nodesrZGΛtbK → uZHΛsbH → tdIΛrXI → sbJΛqZJ