A383084 The number of points in the Euclidean plane that can be determined via a straightedge-and-compass construction using n or fewer lines and circles.

2, 2, 6, 14, 147, 5743, 900487

Offset

0,1

Links

Table of n, a(n) for n=0..6.

Peter Kagey, Illustration of the a(5)=5743 points.

Example

For both n = 0 and n = 1, the a(0) = a(1) = 2 points are the initial points: (0,0) and (1,0).
For n = 2, the a(2) = 6 points are the two above points along with (-1,0), (2,0), (1/2,-sqrt(3)/2), and (1/2,sqrt(3)/2):
  (-1,0): formed by intersecting the line between (0,0) and (1,0) with the circle of radius 1 centered at (0,0).
  (2,0): formed by intersecting the line between (0,0) and (1,0) with the circle of radius 1 centered at (1,0).
  (1/2,-sqrt(3)/2), and (1/2,sqrt(3)/2): formed by intersecting the circle of radius 1 centered at (0,0) with the circle of radius 1 centered at (1,0).

Crossrefs

Cf. A333944, A383082, A383085.

Sequence in context: A390749 A259810 A142471 * A323233 A071208 A231536

Adjacent sequences: A383081 A383082 A383083 * A383085 A383086 A383087

Keyword

nonn,hard,more

Author

Peter Kagey, Apr 16 2025

Status

approved