A349421 Numbers k such that a regular k-gon, when its vertices are connected by infinite lines, creates polygons outside the k-gon with more sides than any polygon inside the k-gon, excluding the central k-sided polygon for odd values of k.

14, 19, 29, 32, 33, 39, 52

Offset: 1

Author

Scott R. Shannon, Nov 17 2021

Keywords

• nonn
• more
• hard

Comments

As a regular k-gon with an odd number of sides always creates a k-sided polygon at the center of the k-gon when its vertices are connected by lines (see A342222), this polygon is excluded when considering the polygons inside the k-gon with the maximum number of sides.

If the next term exists it is greater than 100.

Examples

			14 is a term as when a regular 14-gon's vertices are connected by infinite lines fourteen 6-gons are created outside the vertices while the maximum-sided polygons created inside are 5-gons. See the 14-gon image in A344857.
19 is a term as when a regular 19-gon's vertices are connected by infinite lines nineteen 10-gons are created outside the vertices while the maximum-sided polygons created inside, excluding the central 19-gon, are 8-gons. See the 19-gon image in A344857.
32 is a term as when a regular 32-gon's vertices are connected by infinite lines sixty-four 8-gons are created outside the vertices while the maximum-sided polygons created inside are 7-gons. See the linked image.
		

Links

• Scott R. Shannon, Image for the 32-gon.

Crossrefs

Cf. A344938, A344857, A344311, A007678, A342222.