cp's OEIS Frontend

A198670 Decimal expansion of the least x>0 that gives the absolute minimum of cos(x)+cos(2x)+cos(3x).

%I A198670 #11 Feb 15 2013 09:34:27
%S A198670 1,2,9,2,9,4,3,0,5,8,5,0,5,4,2,6,6,6,5,2,2,5,6,3,1,1,9,5,4,6,9,1,3,5,
%T A198670 4,8,5,4,3,4,6,2,9,7,1,5,0,0,4,7,2,3,7,7,8,6,7,0,2,1,6,2,0,7,4,3,6,7,
%U A198670 3,2,9,0,0,6,1,7,1,9,5,6,5,8,8,0,6,2,0,1,6,0,5,4,6,1,0,7,6,4,3
%N A198670 Decimal expansion of the least x>0 that gives the absolute minimum of cos(x)+cos(2x)+cos(3x).
%C A198670 See A196361 for a guide to related sequences.
%e A198670 x=1.2929430585054266652256311954691354...
%e A198670 min(f(x))=-1.3155651547204494123522707...
%t A198670 n = 3; f[t_] := Cos[t]; s[t_] := Sum[f[k*t], {k, 1, n}];
%t A198670 x = N[Minimize[s[t], t], 110]; u = Part[x, 1]
%t A198670 v = 2 Pi - t /. Part[x, 2]
%t A198670 RealDigits[u]   (* A196361 *)
%t A198670 RealDigits[v]   (* A198670 *)
%t A198670 Plot[s[t], {t, -3 Pi, 3 Pi}]
%t A198670 RealDigits[ ArcSin[ Sqrt[7 + Sqrt[7]/2]/3], 10, 99] // First (* _Jean-François Alcover_, Feb 15 2013 *)
%Y A198670 Cf. A196361.
%K A198670 nonn,cons
%O A198670 1,2
%A A198670 _Clark Kimberling_, Oct 28 2011