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 A385446 #10 Jul 06 2025 11:16:57 %S A385446 9,1,8,0,3,3,9,8,8,7,4,9,8,9,4,8,4,8,2,0,4,5,8,6,8,3,4,3,6,5,6,3,8,1, %T A385446 1,7,7,2,0,3,0,9,1,7,9,8,0,5,7,6,2,8,6,2,1,3,5,4,4,8,6,2,2,7,0,5,2,6, %U A385446 0,4,6,2,8,1,8,9,0,2,4,4,9,7,0,7 %N A385446 Decimal expansion of -7 + 10*phi, with the golden section phi = A001622. %C A385446 This constant d gives the imaginary part of -2*11*Z = c + d*i, where Z is the fixed point of a complex function w (of the loxodromic type) mapping vertices of golden triangles, starting with vertices (D_1, D_2, D_3), circumcribed by the unit circle with center at the origin, and D_1 = i (the complex unit), D_2 = (s - phi*i)/2 and D_3 = (-s - phi*i)/2. This function is w(z) = a*z + b, with a = (-1 + phi) * exp(-3*Pi*i/5) = -((2 - phi) + s*i)/2 and b = (1 - phi)*i, where s = sqrt(3 - phi) = A182007 (the length of the base (D2, D3) of the first triangle). %C A385446 The real part c = (-1 + 3*phi)*s is given in A385445. %C A385446 For details see A385445, and eqs.(5a,b) of the linked paper there. %F A385446 Equals -7 + 10*phi, an integer in the quadratic number field Q(sqrt(5)). %F A385446 Equals 10*A176055-12 = 10*A104457-17 = 10*A001622-7 . - _R. J. Mathar_, Jul 06 2025 %e A385446 9.18033988749894848204586834365638117720309179805762862... %t A385446 RealDigits[10*GoldenRatio - 7, 10, 120][[1]] (* _Amiram Eldar_, Jul 02 2025 *) %Y A385446 Cf. A001622, A182007, A385445. %K A385446 nonn,cons,easy %O A385446 1,1 %A A385446 _Wolfdieter Lang_, Jul 01 2025