A198675 - OEIS

%I #5 Mar 30 2012 18:57:55

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

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

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

%N Decimal expansion of the absolute minimum of cos(x)+cos(2x)+cos(3x)+cos(4x)+cos(5x)+cos(6x).

%C See A196361 for a guide to related sequences.

%e x=0.6926737452063682445569036306595182001...

%e min=-1.940589216902488020962568639391387253030...

%t n = 6; f[t_] := Cos[t]; s[t_] := Sum[f[k*t], {k, 1, n}];

%t x = N[Minimize[s[t], t], 110]; u = Part[x, 1]

%t v = 2 Pi - t /. Part[x, 2]

%t RealDigits[u]  (* A198675 *)

%t RealDigits[v]  (* A198676 *)

%t Plot[s[t], {t, -3 Pi, 3 Pi}, PlotRange -> {-2, 6}]

%Y Cf. A196361, A198676.

%K nonn,cons

%O 1,2

%A _Clark Kimberling_, Oct 28 2011