A208899 Decimal expansion of sqrt(5)/3.

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

Offset: 0

Author

R. J. Mathar, Mar 03 2012

Keywords

• nonn
• cons
• easy

Comments

Equals the absolute value of the cosine of the dihedral angle between two adjacent faces of the regular icosahedron.

Examples

			0.7453559924...
		

Links

• Ivan Panchenko, Table of n, a(n) for n = 0..1000
• Mathematics Stack Exchange, Maximum and Minimum Value of f(x)
• Michael Penn, an "extreme" extreme value problem., YouTube video, 2022.
• Wikipedia, Exsphere

Crossrefs

Cf. A002163, A020837.

Programs

Mathematica

RealDigits[Sqrt[5]/3,10,120][[1]] (* Harvey P. Dale, Jul 03 2013 *)

PARI

first(n) = default(realprecision, max(28, n+10)); digits(((sqrt(5)/3)*10^n)\1) \\ David A. Corneth, Dec 19 2022

Formula

Equals A002163/3 = 20*A020837/3.

Equals Sum_{k>=0} (-1)^k * binomial(2*k,k)/5^k. - Amiram Eldar, Aug 03 2020