A385448 Decimal expansion of sqrt(5 + 7*phi)/sqrt(11), with the golden section phi = A001622.

1, 2, 1, 8, 2, 7, 8, 8, 8, 7, 3, 5, 9, 6, 6, 2, 2, 9, 1, 5, 3, 5, 4, 6, 0, 2, 6, 7, 9, 1, 7, 2, 7, 4, 7, 4, 5, 2, 0, 3, 6, 8, 7, 4, 0, 0, 5, 3, 1, 5, 5, 4, 3, 5, 6, 6, 6, 6, 9, 9, 1, 9, 0, 4, 7, 5, 6, 9, 3, 9, 7, 6, 5, 7, 4, 7, 5, 7, 2, 2, 2, 0, 5, 8

Offset

1,2

Comments

This equals the ratio length(Z, D_1)/s, with the fixed point of a complex loxodromic map w mapping iteratively golden triangles, starting with the one inscribed in a circumcircle with center ot the origin of the complex plane, the top vertex D_1 = i (the complex unit) and the base D_2 = (s - phi*i)/2, D_3 = (-s - phi*i)/2, with s = A182007.

See A385445 for details and a linked paper.

Links

Table of n, a(n) for n=1..84.

Index entries for algebraic numbers, degree 4.

Formula

Equals sqrt(5 + 7*phi)/sqrt(11) = sqrt(5 + 7*phi)/A010468.

Equals A385447/(A010468*A182007).

Minimal polynomial 11*x^4 -17*x^2 +1. - R. J. Mathar, Jun 03 2026\

This ^2 = 1+A391987. - R. J. Mathar, Jun 03 2026

Example

1.218278887359662291535460267917274745203687400531554...

Mathematica

RealDigits[Sqrt[(5 + 7*GoldenRatio)/11], 10, 120][[1]] (* Amiram Eldar, Jul 02 2025 *)

Prog

(PARI) polrootsreal(11*x^4 - 17*x^2 + 1)[4] \\ Charles R Greathouse IV, May 19 2026

Crossrefs

Cf. A001622, A182007, A010468, A385445.

Sequence in context: A363894 A152250 A154175 * A396254 A257777 A011208

Adjacent sequences: A385445 A385446 A385447 * A385449 A385450 A385451

Keyword

nonn,cons,easy

Author

Wolfdieter Lang, Jul 01 2025

Status

approved