A019693 Decimal expansion of 2*Pi/3.

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

Offset

1,1

Comments

Volume between a cylinder and the inscribed sphere of radius 1. - Omar E. Pol, Sep 25 2013

(2/3)*Pi is also the surface area of a sphere whose diameter equals the square root of 2/3. More generally, x*Pi is also the surface area of a sphere whose diameter equals the square root of x. - Omar E. Pol, Jun 18 2018

Volume of a hemisphere of radius 1. - Omar E. Pol, Aug 17 2019

Angle in radians between two vectors of equal magnitude and originating from the same point whose vector sum also has the same magnitude. - Stefano Spezia, Jun 30 2025

References

Mary L. Boas, Mathematical Methods in The Physical Sciences, 3rd Edition, John Wiley & Sons, Inc., 2006. See pp. 687-688.

Links

Ivan Panchenko, Table of n, a(n) for n = 1..1000

Philippe Flajolet and Robert Sedgewick, Analytic Combinatorics, Cambridge Univ. Press, 2009, pp. 235-236.

Amrik Singh Nimbran, Generalized Wallis-Euler products and new infinite products for Pi, Math. Student, Vol. 83, No. 1-4 (2014), pp. 155-164; ResearchGate link.

Index entries for transcendental numbers.

Formula

Equals 5*A019699. - Omar E. Pol, Aug 17 2019

Equals arccos(-1/2). - Amiram Eldar, Aug 12 2020

Equals Integral_{x=-oo..oo} 1/(1 + x^6) dx. - Stefano Spezia, Mar 05 2022

Equals Integral_{x=0..2*Pi} 1/(5 - 4*cos(x)) dx. - Kritsada Moomuang, May 22 2025

Equals Product_{k>=1} (6*k - 4) (6*k)^2/((6*k-5)*(6*k-1)*(6*k+2)) (Nimbran, 2014, p. 159, eq. (15)). - Amiram Eldar, Jul 02 2026

Example

2.094395102393195492308428922186335256131446...

Mathematica

RealDigits[N[2*Pi/3, 6!]] (* Vladimir Joseph Stephan Orlovsky, Dec 02 2009 *)

Prog

(PARI) 2*Pi/3 \\ Michel Marcus, Jun 19 2018

Crossrefs

Cf. A000796, A019692, A019699, A157697.

Sequence in context: A395758 A343882 A168229 * A007493 A262177 A136319

Adjacent sequences: A019690 A019691 A019692 * A019694 A019695 A019696

Keyword

nonn,cons,changed

Author

N. J. A. Sloane

Status

approved