A198675 Decimal expansion of the absolute minimum of cos(x)+cos(2x)+cos(3x)+cos(4x)+cos(5x)+cos(6x).

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, 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, 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

Offset

1,2

Comments

See A196361 for a guide to related sequences.

Links

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

Example

x=0.6926737452063682445569036306595182001...
min=-1.940589216902488020962568639391387253030...

Mathematica

n = 6; 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]  (* A198675 *)
RealDigits[v]  (* A198676 *)
Plot[s[t], {t, -3 Pi, 3 Pi}, PlotRange -> {-2, 6}]

Prog

(PARI) my(t=solve(x=-20, -19, -sin(x)-sin(2*x)*2-sin(3*x)*3-sin(4*x)*4-sin(5*x)*5-sin(6*x)*6)); cos(t)+cos(2*t)+cos(3*t)+cos(4*t)+cos(5*t)+cos(6*t) \\ Charles R Greathouse IV, May 15 2026

Crossrefs

Cf. A196361, A198676.

Sequence in context: A379273 A194562 A239349 * A203131 A381254 A259484

Adjacent sequences: A198672 A198673 A198674 * A198676 A198677 A198678

Keyword

nonn,cons

Author

Clark Kimberling, Oct 28 2011

Status

approved