login
Decimal expansion of the absolute minimum of sin(x)+sin(2x)+sin(3x)+sin(4x).
3

%I #7 Dec 14 2020 12:40:30

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

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

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

%N Decimal expansion of the absolute minimum of sin(x)+sin(2x)+sin(3x)+sin(4x).

%C See A198677 for a guide to related sequences.

%e x=5.764569445617181108633794876455734774725510...

%e min=-3.232384871111452330884269520493428181450...

%t n = 4; 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] (* A198729 *)

%t RealDigits[v] (* A198730 *)

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

%t RealDigits[Minimize[Plus@@Sin[x*Range[4]],x],10,100][[1,1]] (* _Harvey P. Dale_, Dec 14 2020 *)

%Y Cf. A198677.

%K nonn,cons

%O 1,1

%A _Clark Kimberling_, Oct 29 2011