A198729 Decimal expansion of the absolute minimum of sin(x)+sin(2x)+sin(3x)+sin(4x).

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

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}]
RealDigits[Minimize[Plus@@Sin[x*Range[4]],x],10,100][[1,1]] (* Harvey P. Dale, Dec 14 2020 *)