A198678 Decimal expansion of the least x>0 that gives the absolute minimum of sin(x)+sin(2x).

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

Offset: 1

Author

Clark Kimberling, Oct 29 2011

Keywords

• nonn
• cons

Comments

See A198677 for a guide to related sequences.

Examples

			x=2*pi-2*arctan(r), where r=sqrt(6-sqrt(33))
x=5.347255851518260503318727031180159764862...
min=-1.760172593046086919405184649699273192...
		

Crossrefs

Cf. A198677.

Programs

Mathematica

f[t_] := Sin[t]; x = Minimize[f[t] + f[2 t], t]
x = N[Minimize[f[t] + f[2 t], t], 110]; u = Part[x, 1]
v = t /. Part[x, 2]
RealDigits[u]  (* A198677 *)
RealDigits[v]  (* A198678 *)
Plot[f[t] + f[2 t], {t, -3 Pi, 3 Pi}]