A346373 Lowest edge indices of an edge-connected n-gon chain (beginning with n = 3, and increasing by one for each subsequent n-gon), such that no n-gons in the sequence overlap.

1, 2, 3, 3, 3, 4, 5, 4, 5, 6, 6, 6, 7, 7, 8, 8, 9, 8, 10, 10, 10, 11, 11, 12, 11, 14, 12, 15, 13, 13, 16, 16, 15, 17, 16, 17, 17, 18, 20, 18, 21, 18, 20, 21, 22, 22, 22, 23, 22, 24, 23, 25, 25, 27, 25, 27, 25, 28, 26, 30, 29, 29, 30, 30, 30, 31, 30, 33, 32, 34, 34, 33, 36

Offset

1,2

Comments

Joining regular polygons (n-gons) of unit side length, such that each n-gon shares one edge with the previous n-gon, starting with a triangle (3-gon), and increasing n by 1 for each subsequent n-gon, this sequence is a list of indices, a(n), that correspond to the edges of each n-gon in sequence, such that, for each n-gon, a(n) is the smallest possible edge index so as not to allow any n-gon to overlap with any other n-gon. The edge indices for an n-gon are defined as a_n(n) = 1 for the edge that is joined with an edge of a previous n-gon, and increase by 1 for each subsequent edge in a clockwise fashion (or, counterclockwise; the sequence remains identical), up to a_n(n) = n. Then, a(n) = min(a_n(n)), such that the above holds.

It appears a(n) approaches n/2, for large n.

Links

Table of n, a(n) for n=1..73.

Jan Srpčič, First 10 polygons

Jan Srpčič, First 100 polygons

Jan Srpčič, Python code

Crossrefs

Cf. A346112.

Sequence in context: A071112 A097087 A153161 * A238516 A282692 A269371

Adjacent sequences: A346370 A346371 A346372 * A346374 A346375 A346376

Keyword

nonn

Author

Jan Srpčič, Jul 14 2021

Status

approved