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 A321593 #12 Aug 13 2020 14:02:28 %S A321593 4,1,4,3,4,5,4,5,6,7,5,6,4,7,5,7,6,6,5,7,6,7,6,7,5,7,6,8,6,7,6,7,6,7, %T A321593 6,7,5,7,6,7,6,8,7,7,7,6,7,7,6,8,7,7,7,7,7,7,7,8,7,8,5,7,6,7,8,7,7,7, %U A321593 7,7,6,7,6,8,7,7,6,8,7,7,7,8,7,8,7,8,7,8,7,8,6,8,7,8,7,8,7,8,7,8,7,7 %N A321593 Smallest number of vertices supporting a graph with exactly n Hamiltonian paths. %C A321593 The reverse of a path is counted as the same path. a(n) is well-defined as the cycle graph C_n has n paths. %C A321593 a(n) >= A249905(n) - 1, since the number of Hamiltonian paths in G is the same as the number of Hamiltonian cycles in H, where H is G with a new vertex connected to all vertices in G. %H A321593 Jeremy Tan, <a href="/A321593/b321593.txt">Table of n, a(n) for n = 0..2412</a> %H A321593 Erich Friedman, <a href="https://erich-friedman.github.io/mathmagic/0912.html">Math Magic</a> (September 2012). %e A321593 a(12) = 4 since K_4 has 12 Hamiltonian paths, and no graph on less than 4 vertices has 12 Hamiltonian paths. %Y A321593 The corresponding sequence for Hamiltonian cycles is A249905. %K A321593 nonn,hard %O A321593 0,1 %A A321593 _Jeremy Tan_, Nov 14 2018