0,2

A set of points in the plane is called an n-distance set if there are precisely n different distances between pairs of distinct points.

J. H. Conway and N. J. A. Sloane, Lattices with Few Distances, J. Number Theory, 39 (1991), pp. 75-90 [a related paper]

Erdos, Paul, and Fishburn, Peter, Maximum planar sets that determine k distances, Discrete Math. 160 (1996), 115-125.

M. Shinohara, Uniqueness of maximimum planar five-distance sets, Discrete Math., 308 (2008), 3048-3055.

a(1) = 3 from the vertices of an equilateral triangle.

Sequence in context: A046497 A061512 A083964 this_sequence A079091 A038663 A033036

Adjacent sequences: A131625 A131626 A131627 this_sequence A131629 A131630 A131631

nonn,more

njas, May 29 2008

This may be in the OEIS already - with so few terms it is hard to be sure. - njas, May 29 2008