A198671 Decimal expansion of the absolute minimum of cos(x)+cos(2x)+cos(3x)+cos(4x).

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

Offset

1,2

Comments

See A196361 for a guide to related sequences.

Links

Table of n, a(n) for n=1..99.

Example

x=1.002750019227300659428346483723194...
min=-1.519557881642848251369426811329...

Mathematica

n = 4; f[t_] := Cos[t]; s[t_] := Sum[f[k*t], {k, 1, n}];
x = N[Minimize[s[t], t], 110]; u = Part[x, 1]
v = 2 Pi - t /. Part[x, 2]
RealDigits[u]  (* A198671 *)
RealDigits[v] (* A198672 *)
Plot[s[t], {t, -3 Pi, 3 Pi}]
(* Second program: *)
Root[-125 + 600x + 1227x^2 + 512x^3, 1] // RealDigits[#, 10, 99]& // First (* Jean-François Alcover, Feb 19 2013 *)

Crossrefs

Cf. A196361.

Sequence in context: A189234 A199736 A207873 * A129343 A342634 A010482

Adjacent sequences: A198668 A198669 A198670 * A198672 A198673 A198674

Keyword

nonn,cons

Author

Clark Kimberling, Oct 28 2011

Status

approved