cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

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%I A217695 #20 Apr 06 2022 15:21:10
%S A217695 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,
%T A217695 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,
%U A217695 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
%N A217695 Decimal expansion of largest angular separation (in radians) between 13 points on a unit sphere.
%C A217695 Since this is less than Pi/3, the kissing number in three dimensions is 12 rather than 13. Related to the Tammes problem.
%H A217695 Oleg Musin and Alexey Tarasov, <a href="http://arxiv.org/abs/1002.1439">The strong thirteen spheres problem</a>, Discrete & Computational Geometry 48:1 (2012), pp. 128-141. doi:10.1007/s00454-011-9392-2
%e A217695 0.99722359243811916365477045057612201455032449373301442534628103416840073521118... radians = 57.1367030... degrees.
%t A217695 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 *)
%o A217695 (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))
%Y A217695 Cf. A257479.
%K A217695 nonn,cons
%O A217695 0,1
%A A217695 _Charles R Greathouse IV_, Mar 20 2013