A198673 Decimal expansion of the absolute minimum of cos(x)+cos(2x)+cos(3x)+cos(4x)+cos(5x).

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

Offset

0,2

Comments

See A196361 for a guide to related sequences.

Links

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

Example

x=0.8192724134245426759067178580741783999...
min=-1.728768207393169918251228314555655767777...

Mathematica

n = 5; 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] (* A198673 *)
RealDigits[v] (* A198674 *)
Plot[s[t], {t, -3 Pi, 3 Pi}, PlotRange -> {-2, 6}]

Prog

(PARI) my(t=solve(x=0.8125, 0.84375, sin(x)+2*sin(2*x)+3*sin(3*x)+4*sin(4*x)+5*sin(5*x))); cos(t)+cos(2*t)+cos(3*t)+cos(4*t)+cos(5*t) \\ Charles R Greathouse IV, May 16 2026

Crossrefs

Cf. A196361, A198674.

Sequence in context: A107311 A363538 A048836 * A379556 A086236 A244354

Adjacent sequences: A198670 A198671 A198672 * A198674 A198675 A198676

Keyword

nonn,cons

Author

Clark Kimberling, Oct 28 2011

Status

approved