A157697 Decimal expansion of sqrt(2/3).

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

Offset

0,1

Comments

Height (from a vertex to the opposite face) of regular tetrahedron with unit edge. - Stanislav Sykora, May 31 2012

The eccentricity of the ellipse of minimum area that is circumscribing two equal and externally tangent circles (Kotani, 1995). - Amiram Eldar, Mar 06 2022

The standard deviation of a roll of a 3-sided die. - Mohammed Yaseen, Feb 23 2023

References

L. B. W. Jolley, Summation of Series, Dover, 1961, eq. (168) on page 32.

Links

G. C. Greubel, Table of n, a(n) for n = 0..10000

Jisho Kotani, Problem 2053, Crux Mathematicorum, Vol. 5, No. 1 (1995), p. 202; Solution to Problem 2053, by David Hankin, ibid., Vol. 22, No. 4 (1996), pp. 187-188.

D. H. Lehmer, Interesting series involving the Central Binomial Coefficient, Am. Math. Monthly, Vol. 92, No. 7 (1985), pp. 449-457.

Index entries for algebraic numbers, degree 2

Formula

Equals 1 - (1/2)/2 + (1*3)/(2*4)/2^2 - (1*3*5)/(2*4*6)/2^3 + ... [Jolley]

Equals Sum_{n>=0} (-1)^n*binomial(2n,n)/8^n = 1/A115754. Averaging this constant with sqrt(2) = A002193 = Sum_{n>=0} binomial(2n,n)/8^n yields A145439.

From Michal Paulovic, Dec 08 2022: (Start)

Equals 2 * A020763.

Has periodic continued fraction expansion [0, 1, 4; 2, 4]. (End)

Equals exp(-arctanh(1/5)). - Amiram Eldar, Jul 10 2023

Example

0.8164965809277260327324280249...

Maple

evalf(sqrt(2/3)) ;

Mathematica

RealDigits[Sqrt[2/3], 10, 200]][[1]] (* Vladimir Joseph Stephan Orlovsky, Mar 04 2011*)

Prog

(PARI) sqrt(2/3) \\ G. C. Greubel, Mar 30 2018
(Magma) Sqrt(2/3); // G. C. Greubel, Mar 30 2018

Crossrefs

Cf. A002193, A020763, A115754, A145439.

Sequence in context: A019717 A007404 A299627 * A281785 A240982 A258146

Adjacent sequences: A157694 A157695 A157696 * A157698 A157699 A157700

Keyword

cons,easy,nonn

Author

R. J. Mathar, Mar 04 2009

Status

approved