A356252 The smallest number of straight lines that can be used to draw n non-overlapping pentagonal stars.

5, 8, 9, 11, 12, 13

Offset

1,1

Links

Table of n, a(n) for n=1..6.

Nicolay Avilov, Problem Sozvezdiya_iz_pryamykh (in Russian).

Nicolay Avilov, Drawing for a(1)-a(6)

David Consiglio, Jr., 7 stars with 15 lines

Formula

Conjecture: a(n+1) <= a(n)+2 for n > 1. - David Consiglio, Jr., Sep 15 2022

Example

a(1) = 5 because a five-pointed star can be drawn using 5 straight lines.
a(3) = 9 because, given any existing triangle, three five-pointed stars can be drawn using 9 straight lines as follows: through each vertex of the triangle, draw a pair of lines that intersect the opposite side of the triangle in such a way as to divide that side into three line segments of equal length. In addition to these six lines, draw one line parallel to each side of the triangle.
a(7) = 14 or 15. See example of 7 stars with 15 lines. - David Consiglio, Jr., Sep 15 2022

Crossrefs

Sequence in context: A314571 A191977 A349887 * A332245 A101079 A066812

Adjacent sequences: A356249 A356250 A356251 * A356253 A356254 A356255

Keyword

nonn,more

Author

Nicolay Avilov, Jul 31 2022

Status

approved