A198740 - OEIS

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

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

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

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

%N Decimal expansion of the least x>0 that gives 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