Base 64: Cycles Sequences: Maximum Length Cycle Count

Blog: The First Pixel: Kaprekar's Constant 6174

Radix Character Encoding
0123456789ABCDEF
GHIJKLMNOPQRSTUV
WXYZabcdefghijkl
mnopqrstuvwxyzΑΒ

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--
26 cycles6 nodes⮎ Ar → gL → Kh → Mf → Ij → Qb ⮌
31 cycle (fixed) 1 node ⮎ VΒW ⮌
46 cycles8 nodes⮎ 3ΒΒy → y2y4 → wt76 → qlFC → eVVO → FΒΒm → mEmG → YVVU ⮌
53 cycles4 nodes⮎ gKΒgM → hJΒhL → iLΒfK → hMΒeL ⮌
631 cycles35 nodes⮎ eU2yXO → wG2yl6 → wqUWB6 → qf1zMC → yeIiN4 → uQGkb8 → mUAqXG → gW2yVM → wK0Αh6 → ΑqMeB2 → yfHjM4 → uSIiZ8 → mQ6ubG → oWAqVE → ga0ΑRM → ΑK8sh2 → ykMeH4 → uTHjY8 → mS4wZG → sW6uVA → oi0ΑJE → ΑaOcR2 → yE8sn4 → ukYSH8 → mT5vYG → qW4wVC → se0ΑNA → ΑiGkJ2 → yUOcX4 → uE2yn8 → wmYSF6 → qX5vUC → qe2yNC → weGkN6 → qUGkXC ⮌
72 cycles19 nodes⮎ lUEΒmXH → nVGΒkWF → mXEΒmUG → nWHΒjVF → mWDΒnVG → oXGΒkUE → nYFΒlTF → mYHΒjTG → lVFΒlWH → mUFΒlXG → mWGΒkVG → lWEΒmVH → nVFΒlWF → mYFΒlTG → mWHΒjVG → lVDΒnWH → oWFΒlVE → nZFΒlSF → mYIΒiTG ⮌
8191 cycles12 nodes⮎ gaT6uYRM → oK94wshE → sjaMeRIA → iRI8sjaK → kRO8sdaI → kSF8smZI → kXS6uZUI → oS72yuZE → wna6uRE6 → qoZ8sSDC → keb6uQNI → oSHAqkZE ⮌