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

0,2

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.

Links

Table of n, a(n) for n=0..13.

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

Example

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.

Crossrefs

A295774 is the restricted version.

A001212 concerns the one-dimensional problem.

Main diagonal of A306608.

Sequence in context: A070874 A187582 A288553 * A285503 A327221 A014601

Adjacent sequences: A295768 A295769 A295770 * A295772 A295773 A295774

Keyword

nonn,more

Author

Jukka Kohonen, Nov 27 2017

Extensions

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

Status

approved