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 A333717 #19 Sep 08 2020 03:24:43 %S A333717 3,5,4,6,8,5,4,6,8,6,6,5,5,6,6,8,7,6,6,6,6,5,6,6,7,7,7,7,7,6,7,6,6,7, %T A333717 6,6,5,6,6,7,7,7,7,7,7,7,7,7,7,7,7,6,6,6,7,7,7,7,6,7,7,7,6,7,7,7,8,8, %U A333717 7,7,7,8,7,7,7,7,7,7,7,7,7,7,7,7,6,7,7 %N A333717 a(n) is the minimal number of vertices in a simple graph with exactly n cycles. %C A333717 a(n+1) is at most a(n) + 2 since we can add a triangle to a graph with a(n) vertices and increase the number of cycles by 1. %C A333717 David Eppstein observed that an N-gon with each edge replaced by a triangle has 2^N + N cycles and 2N vertices, and gluing such graphs together greedily yields an upper bound on a(n) of O(log n). %H A333717 David Eppstein, <a href="https://mathstodon.xyz/@11011110/104757243863013508">Mathstodon post about O(log n) upper bound</a>, 26 August 2020. %e A333717 For n = 2, a pair of triangles sharing a vertex has five vertices; it is easy to check that no graph on three or four vertices has exactly two cycles, so a(2) = 5. %K A333717 nonn %O A333717 1,1 %A A333717 _Christopher Purcell_, Sep 03 2020