A198672 Decimal expansion of the least x>0 that gives the absolute minimum of cos(x)+cos(2x)+cos(3x)+cos(4x).

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

Offset

1,4

Comments

See A196361 for a guide to related sequences.

Links

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

Index entries for transcendental numbers.

Example

x=1.002750019227300659428346483723194323862...
min(f(x))=-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}]

Prog

(PARI) 2*atan(sqrt(polrootsreal(5*x^3 - 45*x^2 + 63*x - 15)[1])) \\ Charles R Greathouse IV, Apr 09 2026

Crossrefs

Cf. A196361, A198671.

Sequence in context: A348145 A210421 A326098 * A306767 A376621 A113814

Adjacent sequences: A198669 A198670 A198671 * A198673 A198674 A198675

Keyword

nonn,cons

Author

Clark Kimberling, Oct 28 2011

Status

approved