%I #25 Dec 21 2022 20:21:28

%S 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,

%T 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,

%U 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

%N Decimal expansion of sqrt(5)/3.

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

%H Ivan Panchenko, <a href="/A208899/b208899.txt">Table of n, a(n) for n = 0..1000</a>

%H Mathematics Stack Exchange, <a href="https://math.stackexchange.com/questions/413624/maximum-and-minimum-value-of-fx">Maximum and Minimum Value of f(x)</a>

%H Michael Penn, <a href="https://www.youtube.com/watch?v=IM13CpxXgAo">an "extreme" extreme value problem.</a>, YouTube video, 2022.

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Exsphere_%28polyhedra%29">Exsphere</a>

%F Equals A002163/3 = 20*A020837/3.

%F Equals Sum_{k>=0} (-1)^k * binomial(2*k,k)/5^k. - _Amiram Eldar_, Aug 03 2020

%e 0.7453559924...

%t RealDigits[Sqrt[5]/3,10,120][[1]] (* _Harvey P. Dale_, Jul 03 2013 *)

%o (PARI) first(n) = default(realprecision, max(28, n+10)); digits(((sqrt(5)/3)*10^n)\1) \\ _David A. Corneth_, Dec 19 2022

%Y Cf. A002163, A020837.

%K nonn,cons,easy

%O 0,1

%A _R. J. Mathar_, Mar 03 2012