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 A335862 #15 Nov 17 2020 21:22:52
%S A335862 4,5,1,1,4,0,4,6,6,4,2,2,6,7,5,8,1,2,3,3,3,9,2,2,1,4,9,6,8,1,3,1,6,9,
%T A335862 5,7,4,0,2,1,8,4,3,6,1,6,4,5,0,8,8,5,7,4,6,3,5,1,7,4,8,6,8,6,1,2,7,9,
%U A335862 5,8,3,4,4,8,2,1,6,4,9,2,5,1,5,8,9,6,7,5,8,2,7,1,7,4,3,2,5,5,3,3
%N A335862 Decimal expansion of the zero x1 of the cubic polynomial x^3 - 2*x^2 - 10*x - 6.
%C A335862 This cubic polynomial P3(x) = x^3 - 2*x^2 - 10*x - 6 is a factor of the characteristic polynomial F(x) of degree 7 of the 7 X 7 adjacency matrix F7 of the Fano graph with nodes (vertices) of degree 6, 5, 5, 5, 3, 3, 3. See the links for the Fano plane. The graph is in fact planar.
%C A335862 The adjacency matrix is F7 = Matrix([[0, 1, 1, 1, 1, 1, 1], [1, 0, 1, 1, 1, 1, 0], [1, 1, 0, 1, 0, 1, 1], [1, 1, 1, 0, 1, 0, 1], [1, 1, 0, 1, 0, 0, 0], [1, 1, 1, 0, 0, 0, 0], [1, 0, 1, 1, 0, 0, 0]]).
%C A335862 The determinant of F7 is 6. The characteristic polynomial is F(x) = x^7 - 15*x^5 - 26*x^4 + 3*x^3 + 24*x^2 + 2*x - 6 = P3(x)*(x^2 + x - 1)^2. The zeros of F(x) (the eigenvalues or spectrum of F7) are: x1, x2 = -A335863 = -1.752517821..., x3 = -A335864 = -0.7588868422..., twice -1 + phi = 0.618033988..., and twice -phi, where phi = A001622.
%C A335862 For the bipartite incidence graph see the links for the Heawood graph.
%H A335862 Wolfdieter Lang, <a href="https://www.itp.kit.edu/~wl/EISpub/A333852.pdf">A list of representative simple difference sets of the Singer type for small orders m</a>, Karlsruher Institut für Technologie (Karlsruhe, Germany 2020).
%H A335862 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/FanoPlane.html">Fano plane</a>
%H A335862 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/HeawoodGraph.html">Heawood graph</a>
%H A335862 Wikipedia, <a href="https://en.wikipedia.org/wiki/Fano_plane">Fano plane</a>
%H A335862 Wikipedia, <a href="https://de.wikipedia.org/wiki/Heawood-Graph">Heawood graph</a>
%F A335862 x1 = (1/3)*(2 + (179 + 3*sqrt(3)*sqrt(269)*i)^(1/3) + ( 179 - 3*sqrt(3)*sqrt(269)*i)^(1/3)), where i is the imaginary unit.
%e A335862 x1 = 4.5114046642267581233392214968131695740218436164...
%t A335862 With[{k = 3 Sqrt[3] Sqrt[269] I}, First@ RealDigits[Re[(1/3) (2 + (179 + k)^(1/3) + (179 - k)^(1/3))], 10, 100]] (* _Michael De Vlieger_, Nov 17 2020 *)
%Y A335862 Cf. A001622, A335863 (-x2), A335864 (-x3).
%K A335862 nonn,cons,easy
%O A335862 1,1
%A A335862 _Wolfdieter Lang_, Jun 29 2020