A198732 Decimal expansion of the least x>0 that gives the absolute minimum of sin(x)+sin(2x)+sin(3x)+sin(4x)+sin(5x).

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

Offset: 1

Author

Clark Kimberling, Oct 29 2011

Keywords

• nonn
• cons

Comments

See A198677 for a guide to related sequences.

Examples

			x=5.8590231016815427641022649970323299904568...
min=-3.9621733635032856002319779111064909898...
		

Crossrefs

Cf. A198677.

Programs

Mathematica

n = 5; 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]  (* A198731 *)
RealDigits[v] (* A198732 *)
Plot[s[t], {t, -3 Pi, 3 Pi}]