I find it most fascinating looking for the locally maximal densities. Starting from N=2, some arrangements always fall in a "satisfying" pattern and a locally o

I find it most fascinating looking for the locally maximal densities. Starting from N=2, some arrangements always fall in a "satisfying" pattern and a locally optimal maximum density is achieved. "The sequence of N's that establish density records" link leads to an empty page, but this sequence is also known as OEIS A084644 "Best packings of m>1 equal circles into a larger circle setting a new density record", and starts with 2, 3, 4, 7, 19, 37, 55, 85, 121, 147, 148, 150, 151, 187. https://oeis.org/A084644 https://oeis.org/A084644 Look for example at N=1759: http://hydra.nat.uni-magdeburg.de/packing/cci/cci1759.html http://hydra.nat.uni-magdeburg.de/packing/cci/cci1759.html Compare it with N=1758, which has a slight "imperfection": http://hydra.nat.uni-magdeburg.de/packing/cci/cci1758.html http://hydra.nat.uni-magdeburg.de/packing/cci/cci1758.html Or with N=1760, which is too "tight" resulting in a worse density: http://hydra.nat.uni-magdeburg.de/packing/cci/cci1760.html http://hydra.nat.uni-magdeburg.de/packing/cci/cci1760.html