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 A374883 #15 May 29 2025 01:11:51
%S A374883 6,8,5,4,1,0,1,9,6,6,2,4,9,6,8,4,5,4,4,6,1,3,7,6,0,5,0,3,0,9,6,9,1,4,
%T A374883 3,5,3,1,6,0,9,2,7,5,3,9,4,1,7,2,8,8,5,8,6,4,0,6,3,4,5,8,6,8,1,1,5,7,
%U A374883 8,1,3,8,8,4,5,6,7,0,7,3,4,9,1,2,1,6,2
%N A374883 Decimal expansion of phi*(2*phi + 1) (i.e., (7 + 3*sqrt(5))/2), where phi is the golden ratio.
%C A374883 The author conjectures that this is the minimum volume of an axis-aligned bounding box which includes the shortest minimum-link circuit joining all the vertices of the cube {0,1}^3 (i.e., the closed polygonal chains consisting of exactly 6 edges visiting all the points of the set {(0,0,0),(0,0,1),(0,1,0),(0,1,1),(1,0,0),(1,0,1),(1,1,0),(1,1,1)}).
%C A374883 In detail, such a circuit of 6 links is given by (1/2,1+phi,1/2)-((1-phi)/2,0,(1+phi)/2)-((phi+1)/2,0, (1-phi)/2)-(1/2,1+phi,1/2)-((phi+1)/2,0,(phi+1)/2)-((1-phi)/2,0,(1-phi)/2(1/2,1+phi,1/2), where phi := (1+sqrt(5))/2 (see A001622).
%C A374883 Then, phi*(2*phi + 1) = phi^2*(phi + 1) since phi - 1 = 1/phi.
%D A374883 Alfred S. Posamentier, Math Charmers, Tantalizing Tidbits for the Mind, Prometheus Books, NY, 2003, pages 138-139.
%H A374883 Roberto Rinaldi and Marco Ripà, <a href="https://arxiv.org/abs/2212.11216">Optimal cycles enclosing all the nodes of a k-dimensional hypercube</a>, arXiv:2212.11216 [math.CO], 2022.
%H A374883 Marco Ripà, <a href="https://doi.org/10.14710/jfma.v4i2.12053">General uncrossing covering paths inside the Axis-Aligned Bounding Box</a>, Journal of Fundamental Mathematics and Applications, Volume 4, 2021, Number 2, Pages 154-166.
%F A374883 Equals (7 + 3*sqrt(5))/2.
%F A374883 Equals phi^2*(phi + 1), where phi = (1 + sqrt(5))/2.
%F A374883 Equals A104457^2 = 2*A205769. - _Hugo Pfoertner_, Jul 22 2024
%F A374883 Equals A090550 + 1 = A134973 + 5. - _Amiram Eldar_, Jul 23 2024
%F A374883 Equals phi^4. - _Stefano Spezia_, May 28 2025
%e A374883 6.8541019662496845446137605030969...
%t A374883 RealDigits[3*GoldenRatio + 2, 10, 120][[1]] (* _Amiram Eldar_, Jul 23 2024 *)
%Y A374883 Cf. A001622, A090550, A104457, A134973, A205769, A225227, A261547, A363755, A373537, A374149, A374260.
%K A374883 nonn,cons,easy
%O A374883 1,1
%A A374883 _Marco Ripà_, Jul 22 2024