A198676 Decimal expansion of the least x>0 that gives the absolute minimum of cos(x)+cos(2x)+cos(3x)+cos(4x)+cos(5x)+cos(6x).

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

Offset

0,1

Comments

See A196361 for a guide to related sequences.

Links

Table of n, a(n) for n=0..98.

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) solve(x=.6, 1, sin(x)+2*sin(2*x)+3*sin(3*x)+4*sin(4*x)+5*sin(5*x)+6*sin(6*x)) \\ Charles R Greathouse IV, May 16 2026

Crossrefs

Cf. A196361, A198675.

Sequence in context: A289503 A349522 A254135 * A198616 A215668 A344230

Adjacent sequences: A198673 A198674 A198675 * A198677 A198678 A198679

Keyword

nonn,cons

Author

Clark Kimberling, Oct 28 2011

Status

approved