This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A357577 #14 Mar 02 2024 12:27:58 %S A357577 2,7,16,26,42,59,80,104,132,163,194,229,274,312,360,406,465,516,573, %T A357577 637,698,772,838,910,993,1073,1158,1238,1333,1425,1520,1621,1719,1835, %U A357577 1936,2043,2165,2280,2405,2525,2650,2782,2919,3059,3195,3340,3486,3632,3786 %N A357577 Least half area of a convex polygon enclosing a circle with radius n and center (0,0) such that all vertex coordinates are integers. %C A357577 "Enclosing" means that any edge runs outside the circle or is a tangent. %C A357577 Such a polygon does not need to be symmetrical, but the partial areas in the four quadrants are equal. Therefore it is sufficient to find the least area of a quarter polygon (multiplied by 2). The half area is an integer because the area of any convex polygon whose vertex coordinates are integers is a multiple of 1/2. The least number of polygons minimizing the area is 16 if x=y is not an axis of symmetry (2 solutions for each quadrant). %H A357577 Gerhard Kirchner, <a href="/A357577/a357577_1.pdf">Closest polygons around a circle</a> %e A357577 For n=1: 2 X 2 square: a(1) = 4/2 = 2. %e A357577 For n=2: Octagon with vertices (1,2) and (2,1) in the first quadrant: a(2) = 14/2 = 7. %e A357577 For further examples, see "Closest polygons around a circle". %o A357577 (Visual Basic) ' See "Closest polygons around a circle" %Y A357577 Cf. A357575, A357576. %K A357577 nonn %O A357577 1,1 %A A357577 _Gerhard Kirchner_, Oct 17 2022