A377568 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.

1, 2, 4, 5, 8, 9, 10, 16, 18, 20, 32, 36, 49, 81

Offset

1,2

Comments

All of these are sums of two squares.

These distances can be achieved by points on a tilted square lattice.

Links

Table of n, a(n) for n=1..14.

Example

The smallest density of lattice points with distances at least sqrt(5) has density 1/5, so 5 is in the sequence:
o....o.
..o....
....o..
.o....o
...o...
o....o.
But the smallest density of lattice points with distances at least sqrt(13) has density 1/12, so 13 is not in the sequence:
o.....o
.......
...o...
.......
o.....o
.......
...o...

Crossrefs

Subsequence of A001481.

Sequence in context: A010443 A035269 A267703 * A277075 A038558 A286031

Adjacent sequences: A377565 A377566 A377567 * A377569 A377570 A377571

Keyword

nonn,fini,full

Author

Erich Friedman, Nov 04 2024

Status

approved