A198733 Decimal expansion of the absolute minimum of sin(x)+sin(2x)+sin(3x)+sin(4x)+sin(5x)+sin(6x).

4, 6, 9, 0, 3, 6, 1, 8, 0, 3, 9, 5, 3, 9, 4, 1, 7, 1, 9, 1, 6, 9, 5, 6, 7, 7, 6, 7, 6, 7, 7, 3, 0, 7, 4, 6, 0, 8, 9, 1, 1, 5, 1, 8, 4, 1, 9, 4, 7, 9, 0, 9, 4, 7, 4, 6, 2, 8, 4, 8, 4, 5, 2, 7, 3, 5, 0, 9, 7, 4, 8, 1, 2, 8, 1, 4, 2, 9, 3, 3, 6, 6, 4, 3, 5, 8, 7, 8, 4, 2, 0, 4, 9, 5, 7, 9, 1, 4, 6, 3, 2, 7, 8, 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=5.924356380456046882352862563376763567376562...
min=-4.690361803953941719169567767677307460891...
		

Crossrefs

Cf. A198677.

Programs

Mathematica

n = 6; 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]  (* A198733 *)
RealDigits[v] (* A198734 *)
Plot[s[t], {t, -3 Pi, 3 Pi}]
RealDigits[FindMinimum[Plus@@Table[Sin[n*x],{n,6}],{x,.1}, WorkingPrecision -> 100][[1]]][[1]] (* Harvey P. Dale, Dec 08 2015 *)