A198730 Decimal expansion of the least x>0 that gives the absolute minimum of sin(x)+sin(2x)+sin(3x)+sin(4x).

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

Offset: 1

Author

Clark Kimberling, Oct 29 2011

Keywords

• nonn
• cons

Comments

See A198677 for a guide to related sequences.

Examples

			x=5.764569445617181108633794876455734774725510...
min=-3.232384871111452330884269520493428181450...
		

Crossrefs

Cf. A198677.

Programs

Mathematica

n = 4; 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]  (* A198729 *)
RealDigits[v]  (* A198730 *)
Plot[s[t], {t, -3 Pi, 3 Pi}]