cp's OEIS Frontend

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.

%I A346784 #10 Aug 09 2021 04:38:07
%S A346784 0,1,1,3,1,7,49,9,7,13,169,91,4,133,21,361,1729,169,19,7,961,133,9,39,
%T A346784 21793,481,31,9331,301,3367,49,817,13,361,931,1813,63,16
%N 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.
%C A346784 It is conjectured that the number of covered grid points is given by A346126(n-1) for n>2.
%H A346784 Hugo Pfoertner, <a href="http://www.randomwalk.de/sequences/a346126.htm">Examples of self avoiding walks of minimum diameter on the hexagonal lattice</a>.
%e A346784 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, ...
%e A346784 .
%e A346784      Diameter  Covered      R^2 =
%e A346784      of disk   grid        (D/2)^2 =
%e A346784    n    D      points    a(n) / A346785(n)
%e A346784 .
%e A346784    1 0.00000     1        0   /    1
%e A346784    2 1.00000     2        1   /    4
%e A346784    3 1.15470     3        1   /    3
%e A346784    4 1.73205     4        3   /    4
%e A346784    5 2.00000     7        1   /    1
%e A346784    6 2.64575     8        7   /    4
%e A346784    7 2.80000     9       49   /   25
%e A346784    8 3.00000    10        9   /    4
%e A346784    9 3.05505    12        7   /    3
%e A346784   10 3.60555    14       13   /    4
%Y A346784 Corresponding denominators are A346785.
%Y A346784 Cf. A125852, A346126.
%K A346784 nonn,frac,more
%O A346784 1,4
%A A346784 _Hugo Pfoertner_, Aug 08 2021