A386775 Place a point on the integer coordinates, up to |k|, along all four axial directions on a Cartesian plane, and then join an infinite straight line between every pair of points: a(n) is the smallest k such that n lines intersect at a point not on the axes.

2, 3, 4, 6, 8, 9, 9, 10, 14, 16, 18, 20, 24, 25, 26, 30, 34, 36

Offset: 2

Author

Scott R. Shannon, Aug 02 2025

Keywords

• nonn
• more

Comments

See A386559 for images of the graph intersections.

Examples

			a(9) = 10 as the following 9 lines all intersect at the point (4,3) while having |x| and |y| intercepts <= 10 :
.
   equation    |  y-intercept  |  x-intercept
-------------------------------------------------
   -3/2*x + 9  |       9       |       6
       -x + 7  |       7       |       7
   -3/4*x + 6  |       6       |       8
   -1/2*x + 5  |       5       |      10
    1/4*x + 2  |       2       |      -8
    1/2*x + 1  |       1       |      -2
        x - 1  |      -1       |       1
    3/2*x - 3  |      -3       |       2
      3*x - 9  |      -9       |       3
-------------------------------------------------
		

Crossrefs

Cf. A386559.