%I #49 Jun 19 2024 09:37:37
%S 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,
%T 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,
%U 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
%N Decimal expansion of phi*Pi, where phi = (1+sqrt(5))/2.
%C The area of a golden ellipse with a semi-major axis phi and a minor semi-axis 1. - _Amiram Eldar_, Jul 05 2020
%C phi*Pi = area of the region having boundaries y = 0, x = Pi/2, and y = (tan x)^(4/5). - _Clark Kimberling_, Oct 25 2020
%H Harry J. Smith, <a href="/A094886/b094886.txt">Table of n, a(n) for n = 1..20000</a>
%H <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>
%F Equals the nested radical sqrt(Pi^2+sqrt(Pi^4+sqrt(Pi^8+...))). For a proof, see A094885. - _Stanislav Sykora_, May 24 2016
%F Equals Integral_{x=0..Pi/2} tan(x)^(4/5) dx. - _Clark Kimberling_, Nov 18 2020
%e 5.0832036923152598158...
%t First@ RealDigits[N[GoldenRatio Pi, 120]] (* _Michael De Vlieger_, May 24 2016 *)
%o (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
%o (PARI) Pi*(1+sqrt(5))/2 \\ _Michel Marcus_, May 25 2016
%Y Cf. A000796, A001622, A094881, A094885.
%K cons,nonn
%O 1,1
%A _N. J. A. Sloane_, Jun 15 2004