login
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.
3
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
1,4
COMMENTS
It is conjectured that the number of covered grid points is given by A346126(n-1) for n>2.
EXAMPLE
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
CROSSREFS
Corresponding denominators are A346785.
Sequence in context: A282422 A282685 A194583 * A060487 A285020 A165781
KEYWORD
nonn,frac,more
AUTHOR
Hugo Pfoertner, Aug 08 2021
STATUS
approved