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A217695 Decimal expansion of largest angular separation (in radians) between 13 points on a unit sphere. 1
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 (list; constant; graph; refs; listen; history; text; internal format)
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-Fran├žois 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

Sequence in context: A085984 A157245 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

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Last modified January 22 07:30 EST 2020. Contains 331139 sequences. (Running on oeis4.)