A198670 Decimal expansion of the least x>0 that gives the absolute minimum of cos(x)+cos(2x)+cos(3x).

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

Offset

1,2

Comments

See A196361 for a guide to related sequences.

Links

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

Example

x=1.2929430585054266652256311954691354...
min(f(x))=-1.3155651547204494123522707...

Mathematica

n = 3; 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]   (* A196361 *)
RealDigits[v]   (* A198670 *)
Plot[s[t], {t, -3 Pi, 3 Pi}]
RealDigits[ ArcSin[ Sqrt[7 + Sqrt[7]/2]/3], 10, 99] // First (* Jean-François Alcover, Feb 15 2013 *)

Crossrefs

Cf. A196361.

Sequence in context: A171546 A268682 A010699 * A074916 A228375 A188966

Adjacent sequences: A198667 A198668 A198669 * A198671 A198672 A198673

Keyword

nonn,cons

Author

Clark Kimberling, Oct 28 2011

Status

approved