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A295774 a(n) is the minimum size of a restricted planar additive basis for the square [0,2n]^2. 1
1, 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, 68, 72, 76, 80, 84, 88, 92 (list; graph; refs; listen; history; text; internal format)



A planar additive basis for the square [0,2n]^2 is a set of points with nonnegative integer coordinates such that their pairwise sums cover the square. Self-sums are allowed. In a restricted basis all points are in the lower left quadrant [0,n]^2.

Matches A008574 at least up to a(23)=92.


Table of n, a(n) for n=0..23.

J. Kohonen, V. Koivunen and R. Rajamäki, Planar additive bases for rectangles, arXiv preprint arXiv:1711.08812, [math.NT], 2017.

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


a(2)=8: the square [0,4]^2 is covered by the pairwise sums of {(0,0),(1,0),(2,0),(0,1),(2,1),(0,2),(1,2),(2,2)}, which has 8 elements.


A295771 is the nonrestricted version.

Sequence in context: A076310 A161352 A337080 * A008586 A059558 A008574

Adjacent sequences:  A295771 A295772 A295773 * A295775 A295776 A295777




Jukka Kohonen, Nov 27 2017



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Last modified December 8 12:28 EST 2021. Contains 349596 sequences. (Running on oeis4.)