A295771 a(n) is the minimum size of a planar additive basis for the square [0,n]^2.

1, 3, 4, 7, 8, 11, 12, 14, 16, 19, 20, 23, 24, 26

Offset: 0

Author

Jukka Kohonen, Nov 27 2017

Keywords

• nonn
• more

Comments

A planar additive basis is a set of points with nonnegative integer coordinates such that their pairwise sums cover a given rectangle of points with integer coordinates. Pairwise sums of a point with itself are included.

a(n) <= 2n+1, because there is an L-shaped basis of that size.

a(n) <= 2n if n is even and nonzero, because of a square-shaped "boundary basis" with sides at coordinates 0 and n/2.

Examples

			a(3)=7: The square [0,3]^2 is covered by the pairwise sums of the L-shaped basis {(0,0),(1,0),(2,0),(3,0),(0,1),(0,2),(0,3)}, which has 7 elements.
		

Links

• J. Kohonen, V. Koivunen and R. Rajamäki, Planar additive bases for rectangles, Journal of Integer Sequences, 21 (2018), Article 18.9.8.

Crossrefs

A295774 is the restricted version.

A001212 concerns the one-dimensional problem.

Main diagonal of A306608.

Extensions

a(12), a(13) from Jukka Kohonen, Dec 17 2018