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 A383086 #14 Apr 19 2025 08:33:13 %S A383086 1,1,2,4,35,2480 %N A383086 The number of distinct distances between points in the Euclidean plane where the points are constructed via a straightedge-and-compass construction using n circles and no lines. %C A383086 We say that a real number is a constructible number if it is the distance between two points that can be determined from a straightedge-and-compass construction. %C A383086 A straightedge-and-compass construction starts with 2 points marked on the plane, traditionally (0,0) and (1,0). In the constructions counted by this sequence, only the compass is used. Circles can be drawn at any marked point through any other marked point, and new points are marked where circles intersect. %H A383086 Wikipedia, <a href="https://en.wikipedia.org/wiki/Constructible_number">Constructible number</a> %H A383086 Wikipedia, <a href="https://en.wikipedia.org/wiki/Mohr%E2%80%93Mascheroni_theorem">Mohr-Mascheroni theorem</a> %e A383086 For n = 0 and n = 1, the only number that is constructible is 1, the distance between the two initial points. %e A383086 For n = 2, we additionally can construct sqrt(3): draw two unit circles, centered at each of the two starting points. These unit circles intersect in two places, which are a distance of sqrt(3) apart. %e A383086 For n = 3, we additionally can construct 2, and 3. %Y A383086 Cf. A383083, A383085, A383087. %K A383086 nonn,more,hard %O A383086 0,3 %A A383086 _Peter Kagey_, Apr 16 2025