A198743 - OEIS

A198743

Decimal expansion of the absolute minimum of f(x)+f(2x)+f(3x)+f(4x)+f(5x)+f(6x), where f(x)=sin(x)+cos(x).

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

(list; constant; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

See A198735 for a guide to related sequences.

LINKS

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

EXAMPLE

x=5.7523645359132336559108108069560323541652222...

min=-4.7346877027473679719552473484659897598753...

MATHEMATICA

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

n = 6; 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] (* A198743 *)

RealDigits[v] (* A198744 *)

Plot[s[t], {t, -2 Pi, 2 Pi}, PlotRange -> {-5, 8}]

PROG

(PARI) my(t=solve(x=-1, 0, cos(x)-sin(x)+2*cos(2*x)-2*sin(2*x)+3*cos(3*x)-3*sin(3*x)+4*cos(4*x)-4*sin(4*x)+5*cos(5*x)-5*sin(5*x)+6*cos(6*x)-6*sin(6*x))); 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)+sin(6*t)+cos(6*t) \\ Charles R Greathouse IV, May 18 2026

CROSSREFS

Cf. A198735.

Sequence in context: A254397 A197697 A241026 * A271798 A392687 A190357

Adjacent sequences: A198740 A198741 A198742 * A198744 A198745 A198746

KEYWORD

nonn,cons,changed

AUTHOR

Clark Kimberling, Oct 29 2011

STATUS

approved