A094886 - OEIS

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

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OFFSET

1,1

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

LINKS

Harry J. Smith, Table of n, a(n) for n = 1..20000

Index entries for transcendental numbers

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

EXAMPLE

5.0832036923152598158...

MATHEMATICA

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

PROG

(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

CROSSREFS

Cf. A000796, A001622, A094881, A094885.

Sequence in context: A021667 A078119 A085998 * A371506 A371507 A143821

Adjacent sequences: A094883 A094884 A094885 * A094887 A094888 A094889

KEYWORD

cons,nonn

AUTHOR

N. J. A. Sloane, Jun 15 2004

STATUS

approved