A346784 Numerators of minimal squared radii of circular disks covering a record number of lattice points of the hexagonal lattice, when the centers of the circles are chosen to maximize the number of covered lattice points.
0, 1, 1, 3, 1, 7, 49, 9, 7, 13, 169, 91, 4, 133, 21, 361, 1729, 169, 19, 7, 961, 133, 9, 39, 21793, 481, 31, 9331, 301, 3367, 49, 817, 13, 361, 931, 1813, 63, 16
Offset: 1
Examples
0, 1/4, 1/3, 3/4, 1, 7/4, 49/25, 9/4, 7/3, 13/4, 169/48, 91/25, 4, 133/27, 21/4, 361/64, 1729/289, 169/27, 19/3, 7, 961/121, 133/16, 9, 39/4, 21793/2187, ...
.
Diameter Covered R^2 =
of disk grid (D/2)^2 =
n D points a(n) / A346785(n)
.
1 0.00000 1 0 / 1
2 1.00000 2 1 / 4
3 1.15470 3 1 / 3
4 1.73205 4 3 / 4
5 2.00000 7 1 / 1
6 2.64575 8 7 / 4
7 2.80000 9 49 / 25
8 3.00000 10 9 / 4
9 3.05505 12 7 / 3
10 3.60555 14 13 / 4
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