A217695 Decimal expansion of largest angular separation (in radians) between 13 points on a unit sphere.

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

Offset

0,1

Comments

Since this is less than Pi/3, the kissing number in three dimensions is 12 rather than 13. Related to the Tammes problem.

Links

Table of n, a(n) for n=0..100.

Oleg Musin and Alexey Tarasov, The strong thirteen spheres problem, Discrete & Computational Geometry 48:1 (2012), pp. 128-141. doi:10.1007/s00454-011-9392-2

Example

0.99722359243811916365477045057612201455032449373301442534628103416840073521118... radians = 57.1367030... degrees.

Mathematica

digits = 101; x0 = x /. FindRoot[2*Tan[3*Pi/8-x/4]-(1-2*Cos[x])/Cos[x]^2 == 0, {x, 6/5}, WorkingPrecision -> digits+1]; ArcCos[Cos[x0]/(1-Cos[x0])] // RealDigits[#, 10, digits]& // First (* Jean-François Alcover, Feb 20 2014, after PARI *)

Prog

(PARI) (a->acos(cos(a)/(1-cos(a))))(solve(x=1, 2, 2*tan(3*Pi/8-x/4)-(1-2*cos(x))/cos(x)^2))

Crossrefs

Cf. A257479.

Sequence in context: A157245 A334846 A072908 * A197390 A298520 A270712

Adjacent sequences: A217692 A217693 A217694 * A217696 A217697 A217698

Keyword

nonn,cons

Author

Charles R Greathouse IV, Mar 20 2013

Status

approved