cp's OEIS Frontend

A198728 Decimal expansion of the least x>0 that gives the absolute minimum of sin(x)+sin(2x)+sin(3x).

%I A198728 #12 Dec 05 2016 10:40:02
%S A198728 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 A198728 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 A198728 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 A198728 Decimal expansion of the least x>0 that gives the absolute minimum of sin(x)+sin(2x)+sin(3x).
%C A198728 See A198677 for a guide to related sequences.
%e A198728 x=5.615894235655113730430510613029770525768423...
%e A198728 min=-2.499607604320056604368126285618043218243...
%t A198728 n = 3; f[t_] = Sin[t]; s[t_] := Sum[f[k*t], {k, 1, n}];
%t A198728 x = N[Minimize[s[t], t], 110]; u = Part[x, 1]
%t A198728 v = t /. Part[x, 2]
%t A198728 RealDigits[u]  (* A198679 *)
%t A198728 RealDigits[v] (* A198680 *)
%t A198728 Plot[s[t], {t, -3 Pi, 3 Pi}]
%t A198728 (* Second program: *)
%t A198728 RealDigits[3*Pi/2 + ArcSin[Root[-1 - 4x + 2x^2 + 6x^3, 3]], 10, 99] // First (* _Jean-François Alcover_, Feb 15 2013 *)
%Y A198728 Cf. A198677.
%K A198728 nonn,cons
%O A198728 1,1
%A A198728 _Clark Kimberling_, Oct 29 2011