A094886 Decimal expansion of phi*Pi, where phi = (1+sqrt(5))/2.

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

Offset: 1

Author

N. J. A. Sloane, Jun 15 2004

Keywords

• cons
• nonn

Comments

The area of a golden ellipse with a semi-major axis phi and a minor semi-axis 1. - Amiram Eldar, Jul 05 2020

phi*Pi = area of the region having boundaries y = 0, x = Pi/2, and y = (tan x)^(4/5). - Clark Kimberling, Oct 25 2020

Examples

			5.0832036923152598158...
		

Links

• Harry J. Smith, Table of n, a(n) for n = 1..20000
• Index entries for transcendental numbers

Crossrefs

Cf. A000796, A001622, A094881, A094885.

Programs

Mathematica

First@ RealDigits[N[GoldenRatio Pi, 120]] (* Michael De Vlieger, May 24 2016 *)

PARI

{ default(realprecision, 20080); phi=(1+sqrt(5))/2; x=phi*Pi; for (n=1, 20000, d=floor(x); x=(x-d)*10; write("b094886.txt", n, " ", d)); } \\ Harry J. Smith, Apr 27 2009

PARI

Pi*(1+sqrt(5))/2 \\ Michel Marcus, May 25 2016

Formula

Equals the nested radical sqrt(Pi^2+sqrt(Pi^4+sqrt(Pi^8+...))). For a proof, see A094885. - Stanislav Sykora, May 24 2016

Equals Integral_{x=0..Pi/2} tan(x)^(4/5) dx. - Clark Kimberling, Nov 18 2020