A198674 Decimal expansion of the least x>0 that gives the absolute minimum of cos(x)+cos(2x)+cos(3x)+cos(4x)+cos(5x).

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

Offset

0,1

Comments

See A196361 for a guide to related sequences.

Links

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

Index entries for transcendental numbers.

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) 2*atan(sqrt(polrootsreal(15*t^4 - 220*t^3 + 594*t^2 - 396*t + 55)[1])) \\ Charles R Greathouse IV, Apr 20 2026

Crossrefs

Cf. A196361.

Sequence in context: A308043 A286253 A386003 * A168321 A242047 A176455

Adjacent sequences: A198671 A198672 A198673 * A198675 A198676 A198677

Keyword

nonn,cons

Author

Clark Kimberling, Oct 28 2011

Status

approved