A198672 - OEIS

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

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

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

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

%N Decimal expansion of the least x>0 that gives the absolute minimum of cos(x)+cos(2x)+cos(3x)+cos(4x).

%C See A196361 for a guide to related sequences.

%e x=1.002750019227300659428346483723194323862...

%e min(f(x))=-1.519557881642848251369426811329...

%t n = 4; 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] (* A198671 *)

%t RealDigits[v] (* A198672 *)

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

%Y Cf. A196361, A198671.

%K nonn,cons

%O 1,4

%A _Clark Kimberling_, Oct 28 2011