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%I #35 Nov 17 2024 07:29:37
%S 1,2,4,5,8,9,10,16,18,20,32,36,49,81
%N Numbers k with the property that the maximum density of points in the integer lattice with all distances at least sqrt(k) is 1/k.
%C All of these are sums of two squares.
%C These distances can be achieved by points on a tilted square lattice.
%e The smallest density of lattice points with distances at least sqrt(5) has density 1/5, so 5 is in the sequence:
%e o....o.
%e ..o....
%e ....o..
%e .o....o
%e ...o...
%e o....o.
%e But the smallest density of lattice points with distances at least sqrt(13) has density 1/12, so 13 is not in the sequence:
%e o.....o
%e .......
%e ...o...
%e .......
%e o.....o
%e .......
%e ...o...
%Y Subsequence of A001481.
%K nonn,fini,full
%O 1,2
%A _Erich Friedman_, Nov 04 2024