login
Decimal expansion of the absolute minimum of f(x)+f(2x)+f(3x)+f(4x)+f(5x), where f(x)=sin(x)+cos(x).
4

%I #6 Mar 30 2012 18:57:55

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

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

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

%N Decimal expansion of the absolute minimum of f(x)+f(2x)+f(3x)+f(4x)+f(5x), where f(x)=sin(x)+cos(x).

%C See A198735 for a guide to related sequences.

%e x=5.655552158617623094325762837474037558860...

%e min=-4.077697884877698503776497218972682969...

%t f[t_] := Sin[t] + Cos[t]

%t n = 5; 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] (* A198741 *)

%t RealDigits[v] (* A198742 *)

%t Plot[s[t], {t, -2 Pi, 2 Pi}, PlotRange -> {-4.1, 7}]

%Y Cf. A198735.

%K nonn,cons

%O 1,1

%A _Clark Kimberling_, Oct 29 2011