Base 72: 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 cycles9 nodesAz → oL → Sh → Ev → gT → Cx → kP → Kp → Uf
31 cycle (fixed) 1 node ZΚa
42 cycles3 nodese7ΒW → u7ΒG → udVG
52 cycles2 nodesaYΚaa → aΚΚΚZ
68 cycles47 nodesM2ΚΚΗo → ΘnHrM3 → ΕaQiZ6 → yI0ΙrC → ΙmYaN2 → ΗP1Θk4 → ΗΓKo74 → ΓvTfE8 → uhBxSG → meEuVO → gO8ΑlU → sNBxmI → maOkZO → OM0Ιnm → ΙRNli2 → ΗOGsl4 → ΓcMmX8 → uQ4ΕjG → ΑeIqVA → qY8ΑbK → sW2ΗdI → Εa6ΓZ6 → yw0ΙDC → ΙmiQN2 → ΗPHrk4 → ΓaKoZ8 → uU0ΙfG → ΙeAyV2 → Ηo8ΑL4 → ΓsSgH8 → ubDvYG → ie2ΗVS → ΕG8Αt6 → yscWHC → mb5ΔYO → yO2ΗlC → ΕmMmN6 → yQOkjC → mMIqnO → YRNlic → OH3Ζsm → ΓbNlY8 → uO2ΗlG → ΕeMmV6 → yQ8ΑjC → smIqNI → aYOkba
72 cycles19 nodesrYGΚsbJ → tZIΚqaH → sbGΚsYI → taJΚpZH → saFΚtZI → ubIΚqYG → tcHΚrXH → scJΚpXI → rZHΚraJ → sYHΚrbI → saIΚqZI → raGΚsZJ → tZHΚraH → scHΚrXI → saJΚpZI → rZFΚtaJ → uaHΚrZG → tdHΚrWH → scKΚoXI