A198744 - OEIS

%I #5 Mar 30 2012 18:57:55

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

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

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

%N Decimal expansion of the least x>0 that gives the absolute minimum of f(x)+f(2x)+f(3x)+f(4x)+f(5x)+f(6x), where f(x)=sin(x)+cos(x).

%C See A198735 for a guide to related sequences.

%e x=5.7523645359132336559108108069560323541652222...

%e min=-4.7346877027473679719552473484659897598753...

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

%t n = 6; 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] (* A198743 *)

%t RealDigits[v] (* A198744 *)

%t Plot[s[t], {t, -2 Pi, 2 Pi}, PlotRange -> {-5, 8}]

%Y Cf. A198735.

%K nonn,cons

%O 1,1

%A _Clark Kimberling_, Oct 29 2011