cp's OEIS Frontend

A346993 Record numbers of grid points in a square lattice covered by a continuously growing circular disk if the center of the disk is chosen to cover the maximum possible number of grid points.

%I A346993 #17 Aug 24 2021 14:37:45
%S A346993 1,2,4,5,6,7,9,12,13,14,16,17,21,22,24,26,27,28,32,33,37,38,39,40,41,
%T A346993 44,45,46,47,48,52,56,57,58,59,61,62,63,64,65,69,70,71,72,73,74,76,77,
%U A346993 78,79,80,81,82,83,84,85,89,90,91,92,93,94,97,98,99,100,104,112,113
%N A346993 Record numbers of grid points in a square lattice covered by a continuously growing circular disk if the center of the disk is chosen to cover the maximum possible number of grid points.
%H A346993 Hugo Pfoertner, <a href="http://www.randomwalk.de/sequences/a346993.pdf">Visualization of configurations with maximum number of covered grid points</a>.
%e A346993      Diameter  Covered      R^2 =
%e A346993      of disk   grid        (D/2)^2 =
%e A346993    n    D      points  A346994(n)/A346995(n)
%e A346993 .
%e A346993    1 0.00000     1           0   /    1
%e A346993    2 1.00000     2           1   /    4
%e A346993    3 1.41421     4           1   /    2
%e A346993    4 2.00000     5           1   /    1
%e A346993    5 2.23607     6           5   /    4
%e A346993    6 2.50000     7          25   /   16
%e A346993    7 2.82843     9           2   /    1
%e A346993    8 3.16228    12           5   /    2
%e A346993    9 3.67696    13         169   /   50
%e A346993   10 3.80058    14          65   /   18
%e A346993   11 4.12311    16          17   /    4
%e A346993   12 4.33333    17         169   /   36
%e A346993   13 4.47214    21           5   /    1
%Y A346993 The corresponding squared radii are A346994/A346995.
%Y A346993 Cf. A053411, A053414, A053415, A123690, A346124.
%K A346993 nonn
%O A346993 1,2
%A A346993 _Hugo Pfoertner_, Aug 16 2021