cp's OEIS Frontend

A198677 Decimal expansion of the absolute minimum of sin(x)+sin(2x).

%I A198677 #11 Feb 19 2013 04:26:47
%S A198677 1,7,6,0,1,7,2,5,9,3,0,4,6,0,8,6,9,1,9,4,0,5,1,8,4,6,4,9,6,9,9,2,7,3,
%T A198677 1,9,2,0,7,7,2,5,5,5,0,9,8,7,9,8,4,6,7,9,3,2,9,1,8,5,0,9,4,1,8,3,6,7,
%U A198677 8,4,6,7,7,1,9,9,4,7,9,9,3,1,6,9,1,0,9,0,9,5,2,8,9,3,8,8,9,8,0
%N A198677 Decimal expansion of the absolute minimum of sin(x)+sin(2x).
%C A198677 The function f(x)=sin(x)+sin(2x)+...+sin(nx), where n>=2, attains an absolute minimum, m, at some c between 0 and 2*pi.  The absolute maximum, -m, occurs at 2*pi-c. Guide to related sequences (including graphs in Mathematica programs):
%C A198677 n....x.........minimum of f(x)
%C A198677 2....A198677...A198678
%C A198677 3....A198679...A198728
%C A198677 4....A198729...A198730
%C A198677 5....A198731...A198732
%C A198677 6....A198733...A198734
%e A198677 x=5.347255851518260503318727031180159764862...
%e A198677 min=-1.760172593046086919405184649699273192...
%t A198677 f[t_] := Sin[t]; x = Minimize[f[t] + f[2 t], t]
%t A198677 x = N[Minimize[f[t] + f[2 t], t], 110]; u = Part[x, 1]
%t A198677 v = t /. Part[x, 2]
%t A198677 RealDigits[u]  (* A198677 *)
%t A198677 RealDigits[v]  (* A198678 *)
%t A198677 Plot[f[t] + f[2 t], {t, -3 Pi, 3 Pi}]
%t A198677 -Sqrt[3*(69 + 11*Sqrt[33])/2]/8 // RealDigits[#, 10, 99]& // First (* _Jean-François Alcover_, Feb 19 2013 *)
%Y A198677 Cf. A198678.
%K A198677 nonn,cons
%O A198677 1,2
%A A198677 _Clark Kimberling_, Oct 29 2011