A393937 Start with a single point at the origin of the square grid. At each step, add a point adjacent to an existing point in such a way that the maximum number of existing points on a line through the new point is as small as possible. In case of ties, compare the number of points on the line with the next largest number of points, etc. If there is still a tie, choose the lexicographically largest point. a(n) is the number of points that have been added when n collinear points first appear.

1, 2, 5, 15, 31, 51, 75, 109, 142, 293, 348, 408, 477, 597, 691, 1128, 1312, 1783, 1978, 2151, 2329, 3581, 4249, 4556

Offset

1,2

Comments

Two points are adjacent if they differ by 1 in a single coordinate (von Neumann neighborhood).

For the first 5000 points, the tiebreaking rule that considers the lexicographical ordering is necessary only when points 2-10, 16, 21, 24, 25, 36, 51, 52, and 55 are added.

Although there is a larger number of cells to choose from in each step compared to A393935, a(n) < A393935(n) for n = 9 and 11 <= n <= 24.

Links

Table of n, a(n) for n=1..24.

Pontus von Brömssen, The first 142 points numbered in order of appearance, with record setters in red.

Pontus von Brömssen, The first 1000 points, with record setters in red.

Formula

a(n) <= A380991(n-1)+1 for n >= 2.

Crossrefs

Cf. A380991, A393935, A393939.

Sequence in context: A191313 A078528 A309272 * A077686 A034499 A299159

Adjacent sequences: A393934 A393935 A393936 * A393938 A393939 A393940

Keyword

nonn,more

Author

Pontus von Brömssen, Mar 04 2026

Status

approved