1,6

The position of weight 1 is kept fixed at position 1. Mirror configurations are counted only once. For n not a prime power, the sequence equals A118887.

G. J. Woeginger, Nothing new about equiangular polygons, Amer. Math. Monthly, 120 (2013), 849-850.

a(5)=1: The configuration minimizing the remaining imbalance with respect to the center of the circle is [1 4 3 2 5] (and its mirror image).

Examples of minimum imbalance configurations not in A118887:

a(7)=1: [1 4 7 2 3 5 6];

a(8)=2: [1 4 7 3 6 2 5 8], [1 7 4 3 6 5 2 8];

a(9)=3: [1 5 9 2 7 3 4 8 6], [1 5 9 4 2 6 7 3 8], [1 6 5 4 9 2 3 7 8];

a(11)=1: [1 8 9 5 2 6 10 7 3 4 11];

a(13)=1: [1 2 7 12 13 4 5 3 8 6 11 9 10];

a(16)=144: lexicographically earliest [1 3 5 13 16 7 10 2 14 4 6 9 12 8 11 15];

a(17)=2: [1 7 3 17 10 9 15 2 14 6 5 4 16 8 13 12 11],

[1 8 9 3 16 4 12 13 14 2 10 5 6 7 17 11 15] and their mirror configurations (e.g. [1 11 12 13 8 ...]) both produce a center of gravity with distance 2.1884*10^(-7) from the center of a circle with radius 1. All other configurations produce greater distances, e.g. [1 3 11 16 9 5 7 12 14 4 10 8 2 15 13 6 17] -> 2.5126*10^(-7). - Hugo Pfoertner, Oct 24 2019

Cf. A118887, A326921.

Sequence in context: A350026 A391806 A382273 * A061678 A206425 A227428

Adjacent sequences: A118885 A118886 A118887 * A118889 A118890 A118891

hard,more,nonn

Hugo Pfoertner, May 26 2006

a(17) corrected by Hugo Pfoertner, Oct 24 2019

a(18) from Max Alekseyev, Mar 19 2026

approved