A198753 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).

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

Offset

1,1

Comments

See A198745 for a guide to related sequences.

Links

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

Example

x=6.1023848080560582664529077489592541...
min=-7.9923425075026144580650827802488965...

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]  (* A198753 *)
RealDigits[v]  (* A198754 *)
Plot[s[t], {t, -2 Pi, 2 Pi}, PlotRange -> {-9, 5}]

Prog

(PARI) my(t=solve(x=-0.5, 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. A198745.

Sequence in context: A371135 A021930 A200103 * A244625 A363906 A388925

Adjacent sequences: A198750 A198751 A198752 * A198754 A198755 A198756

Keyword

nonn,cons

Author

Clark Kimberling, Oct 29 2011

Status

approved