A385447 Decimal expansion of sqrt(8 + 9*phi), with the golden section A001622.

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

Offset: 1

Author

Wolfdieter Lang, Jul 01 2025

Keywords

• nonn
• cons
• easy

Comments

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.

See A385445 for details and the linked paper, eq. (7b).

Examples

			4.7499795682454312672720369270371548927...
		

Crossrefs

Cf. A001622, A182007, A385445, A385446.

Programs

Mathematica

RealDigits[Sqrt[8 + 9*GoldenRatio], 10, 120][[1]] (* Amiram Eldar, Jul 02 2025 *)

Formula

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.