|
%I #6 Mar 30 2012 18:57:56
%S 5,3,7,1,0,1,6,7,7,8,2,4,5,6,8,0,5,8,5,8,0,1,2,9,8,6,6,0,9,1,4,4,0,4,
%T 4,5,8,3,3,7,9,1,9,2,4,8,6,2,4,4,2,0,3,4,4,0,6,5,5,6,3,3,9,9,9,2,1,7,
%U 1,4,2,2,7,6,1,9,5,3,1,4,9,6,7,0,8,7,2,0,5,9,1,1,2,6,3,7,1,8,8
%N Decimal expansion of the absolute minimum of f(x)+f(2x)+f(3x)+f(4x), where f(x)=sin(x)-cos(x).
%C See A198745 for a guide to related sequences.
%e x=6.02199019639758406905296413941959795147011...
%e min=-5.37101677824568058580129866091440445833...
%t f[t_] := Sin[t] - Cos[t]
%t n = 4; 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] (* A198749 *)
%t RealDigits[v] (* A198750 *)
%t Plot[s[t], {t, -2 Pi, 2 Pi}, PlotRange -> {-6, 4}]
%Y Cf. A198745.
%K nonn,cons
%O 1,1
%A _Clark Kimberling_, Oct 29 2011
|
