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 A386251 #22 Aug 06 2025 00:07:55 %S A386251 60,28,20,22,18,16,18,18,16,18,18,18,20,20,18,20,20,20,22,22,22,24,24, %T A386251 22,24,24,24,26,24,24,26,26,26,26,26,26,28,28,28,28,30,28,30,30,30,30, %U A386251 30,30,32,32,32,32,32,32,32,34,34,34,34,34,36,34,34,36,36 %N A386251 Consider the graph whose vertices are the points of the n-dimensional cubic lattice with points connected by all integer-length diagonals that traverse all n dimensions and do not intersect intermediate points. a(n) is the total length of the shortest possible closed walk in this graph via noncongruent diagonals. %C A386251 It is provable that all such walks must be even in total length. It is also provable that 3-segment closed walks are impossible for n < 6, and conjectured that a(n) for all n >= 6 are produced by 3-segment walks. %C A386251 For n = 2, the walk segments are the hypotenuses of noncongruent primitive Pythagorean triangles. %C A386251 The offset is 2, because even though the graph could be defined in dimension 1 (the vertices would be the points of Z, with each point connected to its two neighbors), it would not contain any closed paths. %C A386251 Adding a constraint that the diagonal segments must all have the same length gives A385525. %H A386251 Charles L. Hohn, <a href="/A386251/a386251.png">a(2), graphical view</a> %H A386251 Charles L. Hohn, <a href="/A386251/a386251.gif">a(3), graphical view, animated</a> %e A386251 a(2) = 60 because [3, 4] + [5, 12] + [-15, 8] + [7, -24] = [0, 0] and segment lengths 5 + 13 + 17 + 25 = 60, which is the smallest example for n = 2. %e A386251 a(3) = 28: [2, 2, 1] + [-3, -2, -6] + [-7, 4, 4] + [8, -4, 1] = [0, 0, 0] and 3 + 7 + 9 + 9 = 28. %e A386251 a(4) = 20: [1, 1, 1, 1] + [-1, -2, -2, -4] + [-5, -3, -1, 1] + [5, 4, 2, 2] = [0, 0, 0, 0] and 2 + 5 + 6 + 7 = 20. %Y A386251 Cf. A385525. %Y A386251 Cf. A020882 (diagonals in 2 dimensions), A096910 (diagonals in 3 dimensions). %K A386251 nonn,nice %O A386251 2,1 %A A386251 _Charles L. Hohn_, Jul 16 2025