A198679 Decimal expansion of the absolute minimum of sin(x)+sin(2x)+sin(3x).

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

Offset: 1

Author

Clark Kimberling, Oct 29 2011

Keywords

• nonn
• cons

Comments

See A198677 for a guide to related sequences.

Examples

			x=5.615894235655113730430510613029770525768423...
min=-2.499607604320056604368126285618043218243...
		

Crossrefs

Cf. A198677.

Programs

Mathematica

n = 3; f[t_] = Sin[t]; s[t_] := Sum[f[k*t], {k, 1, n}];
x = N[Minimize[s[t], t], 110]; u = Part[x, 1]
v = t /. Part[x, 2]
RealDigits[u]  (* A198679 *)
RealDigits[v] (* A198680 *)
Plot[s[t], {t, -3 Pi, 3 Pi}]
(* Second program: *)
Root[-108 + 2124x^2 - 4892x^4 + 729x^6, 1] // RealDigits[#, 10, 99]& // First (* Jean-François Alcover, Feb 19 2013 *)