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 A385447 #13 Jul 03 2025 08:58:02 %S A385447 4,7,4,9,9,7,9,5,6,8,2,4,5,4,3,1,2,6,7,2,7,2,0,3,6,9,2,7,0,3,7,1,5,4, %T A385447 8,9,2,7,7,4,6,6,1,6,7,4,6,8,8,0,8,9,8,0,6,1,0,3,4,2,6,0,3,9,5,7,4,1, %U A385447 8,8,3,2,4,0,1,1,6,5,9,9,4,0,9,5 %N A385447 Decimal expansion of sqrt(8 + 9*phi), with the golden section A001622. %C A385447 This constant c gives sqrt(11)*rho_1, where rho_1 = length(Z, D_1), with the fixed point Z = -(A385445 + A385446*i)/(2*11) of the complex map w given in A385445 and D_1 = i. %C A385447 See A385445 for details and the linked paper, eq. (7b). %F A385447 Equals sqrt(8 + 9*phi) = sqrt(5 + 7*phi)*s, with s = A182007, the length of the side of a regular pentagon circumcribed by a unit circle. %e A385447 4.7499795682454312672720369270371548927... %t A385447 RealDigits[Sqrt[8 + 9*GoldenRatio], 10, 120][[1]] (* _Amiram Eldar_, Jul 02 2025 *) %Y A385447 Cf. A001622, A182007, A385445, A385446. %K A385447 nonn,cons,easy %O A385447 1,1 %A A385447 _Wolfdieter Lang_, Jul 01 2025