Base 60: 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--
21 cycle 30 nodes0x → w1 → u3 → q7 → iF → SV → 2v → s5 → mB → aN → Cl → YP → 8p → gH → OZ → An → cL → Gh → QX → 6r → kD → WR → 4t → o9 → eJ → Kd → If → Mb → Ej → UT
31 cycle (fixed) 1 node TxU
47 cycles4 nodesK3te → qJd8 → iJdG → SJdW
52 cycles2 nodesUSxUU → UxxxT
66 cycles66 nodesG62uri → slRVC6 → mZ3tOC → qaAmN8 → icCkLG → YSGgVQ → Q82upY → sh7pG6 → miQWFC → aT5rUO → mC0wlC → waYON2 → uD9nk4 → qeWQJ8 → iL5rcG → mSGgVC → aQ2uXO → sC6ql6 → mkYODC → aX9nQO → eC6qlK → kZJdOE → WKAmdS → cJ3teM → qLFhc8 → iSGgVG → SQ2uXW → s73tq6 → qmiEB8 → ibTTMG → SExxiW → jVBlSF → aU2uTO → sC0wl6 → wmYOB2 → ub9nM4 → qeEiJ8 → iUKcTG → SI0wfW → wN3ta2 → uqCk74 → qjXPE8 → iV7pSG → iS2uVG → sS2uV6 → sm2uB6 → smaMB6 → mbDjMC → aWEiRO → UC4slU → oYxxOA → nZFhOB → cSAmVM → cG2uhM → sRFhW6 → mS4sVC → oa2uNA → seCkJ6 → mYKcPC → aI8ofO → gNBlaI → aOCkZO → YCAmlQ → cZ7pOM → iGAmhG → cSQWVM
72 cycles19 nodesiSDxjVG → kTFxhUE → jVDxjSF → kUGxgTE → jUCxkTF → lVFxhSD → kWExiRE → jWGxgRF → iTExiUG → jSExiVF → jUFxhTF → iUDxjTG → kTExiUE → jWExiRF → jUGxgTF → iTCxkUG → lUExiTD → kXExiQE → jWHxfRF
89 cycles20 nodesWUN2uaTS → sD40wtk6 → wpmWQB82 → uhb5rMG4 → qmREiWB8 → ibU4sTMG → oSF0wiVA → weT2uUJ2 → usL0wc54 → wqnGgA72 → ujdPXKE4 → qVJ7peS8 → jhL2ucGF → sURGgWT6 → mQ50wsXC → wna6qNA2 → ukdCkKD4 → qYXIeQP8 → iM96qobG → kfSEiVIE