A198751 - OEIS

%I #5 Mar 30 2012 18:57:56

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

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

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

%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 A198745 for a guide to related sequences.

%e x=6.069500393967011029293576253857045423823...

%e min=-6.682126364889810370734279330610851580...

%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] (* A198751 *)

%t RealDigits[v] (* A198752 *)

%t Plot[s[t], {t, -2 Pi, 2 Pi}, PlotRange -> {-7, 4.5}]

%Y Cf. A198745.

%K nonn,cons

%O 1,1

%A _Clark Kimberling_, Oct 29 2011