A198739 - OEIS

%I #7 Mar 30 2012 18:57:55

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

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

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

%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 A198735 for a guide to related sequences.

%e x=5.5154369780827950192498750534181150758000...

%e min=-3.4194065057629463327304557162112432637...

%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] (* A198739 *)

%t RealDigits[v] (* A198740 *)

%t Plot[s[t], {t, -3 Pi, 3 Pi}]

%Y Cf. A198735.

%K nonn,cons

%O 1,1

%A _Clark Kimberling_, Oct 29 2011