A198741 Decimal expansion of the absolute minimum of f(x)+f(2x)+f(3x)+f(4x)+f(5x), where f(x)=sin(x)+cos(x).

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

Offset

1,1

Comments

See A198735 for a guide to related sequences.

Links

Table of n, a(n) for n=1..99.

Example

x=5.655552158617623094325762837474037558860...
min=-4.077697884877698503776497218972682969...

Mathematica

f[t_] := Sin[t] + Cos[t]
n = 5; s[t_] := Sum[f[k*t], {k, 1, n}]
x = N[Minimize[s[t], t], 110]; u = Part[x, 1]
v = t /. Part[x, 2]
RealDigits[u] (* A198741 *)
RealDigits[v] (* A198742 *)
Plot[s[t], {t, -2 Pi, 2 Pi}, PlotRange -> {-4.1, 7}]

Prog

(PARI) my(t=solve(x=-1, 0, cos(x)-sin(x)+cos(2*x)*2-sin(2*x)*2+cos(3*x)*3-sin(3*x)*3+cos(4*x)*4-sin(4*x)*4+cos(5*x)*5-sin(5*x)*5)); sin(t)+cos(t)+sin(2*t)+cos(2*t)+sin(3*t)+cos(3*t)+sin(4*t)+cos(4*t)+sin(5*t)+cos(5*t) \\ Charles R Greathouse IV, May 10 2026

Crossrefs

Cf. A198735.

Sequence in context: A196533 A200518 A016682 * A298617 A221596 A195286

Adjacent sequences: A198738 A198739 A198740 * A198742 A198743 A198744

Keyword

nonn,cons

Author

Clark Kimberling, Oct 29 2011

Status

approved