%I #11 Dec 05 2016 10:40:09

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

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

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

%N Decimal expansion of the absolute minimum of sin(x)+sin(2x)+sin(3x).

%C See A198677 for a guide to related sequences.

%e x=5.615894235655113730430510613029770525768423...

%e min=-2.499607604320056604368126285618043218243...

%t n = 3; f[t_] = Sin[t]; s[t_] := Sum[f[k*t], {k, 1, n}];

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

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

%t RealDigits[u] (* A198679 *)

%t RealDigits[v] (* A198680 *)

%t Plot[s[t], {t, -3 Pi, 3 Pi}]

%t (* Second program: *)

%t Root[-108 + 2124x^2 - 4892x^4 + 729x^6, 1] // RealDigits[#, 10, 99]& // First (* _Jean-François Alcover_, Feb 19 2013 *)

%Y Cf. A198677.

%K nonn,cons

%O 1,1

%A _Clark Kimberling_, Oct 29 2011