A198747 - OEIS

A198747

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

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

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

OFFSET

1,1

COMMENTS

See A198745 for a guide to related sequences.

LINKS

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

EXAMPLE

x=5.94730029228227831501115084260797711836331...

min=-4.05824487647797618374998236242336948409...

MATHEMATICA

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

n = 3; 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] (* A198747 *)

RealDigits[v] (* A198748 *)

Plot[s[t], {t, -2 Pi, 2 Pi}, PlotRange -> {-4.1, 3}]

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))); sin(t)-cos(t)+sin(2*t)-cos(2*t)+sin(3*t)-cos(3*t) \\ Charles R Greathouse IV, May 18 2026

CROSSREFS

Cf. A198745.

Sequence in context: A388372 A180309 A102293 * A021965 A372274 A355921

Adjacent sequences: A198744 A198745 A198746 * A198748 A198749 A198750

KEYWORD

nonn,cons,changed

AUTHOR

Clark Kimberling, Oct 29 2011

STATUS

approved