|
%I #5 Mar 30 2012 18:57:56
%S 6,1,0,2,3,8,4,8,0,8,0,5,6,0,5,8,2,6,6,4,5,2,9,0,7,7,4,8,9,5,9,2,5,4,
%T 1,7,9,5,3,7,4,1,1,9,2,6,0,9,6,6,5,6,9,0,9,0,4,7,9,5,5,7,3,6,0,0,9,0,
%U 5,0,1,4,0,6,4,1,1,6,1,2,6,6,2,6,4,6,4,6,9,7,8,1,6,0,4,8,7,0,8
%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 A198745 for a guide to related sequences.
%e x=6.1023848080560582664529077489592541...
%e min=-7.9923425075026144580650827802488...
%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] (* A198753 *)
%t RealDigits[v] (* A198754 *)
%t Plot[s[t], {t, -2 Pi, 2 Pi}, PlotRange -> {-9, 5}]
%Y Cf. A198745.
%K nonn,cons
%O 1,1
%A _Clark Kimberling_, Oct 29 2011
|
