login
Decimal expansion of the least x>0 that gives the absolute minimum of sin(x)+sin(2x)+sin(3x).
1

%I #12 Dec 05 2016 10:40:02

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

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

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

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

%C See A198677 for a guide to related sequences.

%e x=5.615894235655113730430510613029770525768423...

%e min=-2.499607604320056604368126285618043218243...

%t n = 3; f[t_] = Sin[t]; s[t_] := Sum[f[k*t], {k, 1, n}];

%t x = N[Minimize[s[t], t], 110]; u = Part[x, 1]

%t v = t /. Part[x, 2]

%t RealDigits[u] (* A198679 *)

%t RealDigits[v] (* A198680 *)

%t Plot[s[t], {t, -3 Pi, 3 Pi}]

%t (* Second program: *)

%t RealDigits[3*Pi/2 + ArcSin[Root[-1 - 4x + 2x^2 + 6x^3, 3]], 10, 99] // First (* _Jean-François Alcover_, Feb 15 2013 *)

%Y Cf. A198677.

%K nonn,cons

%O 1,1

%A _Clark Kimberling_, Oct 29 2011