A198744 - OEIS

A198744

Decimal expansion of the least x>0 that gives the absolute minimum of f(x)+f(2x)+f(3x)+f(4x)+f(5x)+f(6x), where f(x)=sin(x)+cos(x).

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

(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.

Index entries for transcendental numbers.

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) solve(x=5.5, 6, 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)) \\ Charles R Greathouse IV, May 17 2026

CROSSREFS

Cf. A198735.

Sequence in context: A242059 A178668 A390068 * A201944 A377932 A165242

Adjacent sequences: A198741 A198742 A198743 * A198745 A198746 A198747

KEYWORD

nonn,cons,changed

AUTHOR

Clark Kimberling, Oct 29 2011

STATUS

approved