A198737 - OEIS

%I #8 Mar 27 2022 14:48:53

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

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

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

%N Decimal expansion of the absolute minimum of f(x)+f(2x)+f(3x), where f(x)=sin(x)+cos(x).

%C See A198735 for a guide to related sequences.

%e x=5.2944289469521176405605333970464500...

%e min=-2.7587311916385540011189353581492...

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

%t n = 3; 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]  (* A198737 *)

%t RealDigits[v]  (* A198738 *)

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

%t RealDigits[Abs[NMinimize[Sin[x]+Cos[x]+Sin[2x]+Cos[2x]+Sin[3x]+Cos[3x],x,WorkingPrecision-> 100][[1]]],10,100][[1]] (* _Harvey P. Dale_, Mar 27 2022 *)

%Y Cf. A198735.

%K nonn,cons

%O 1,1

%A _Clark Kimberling_, Oct 29 2011