A198752 Decimal expansion of the least x>0 that gives the absolute minimum of f(x)+f(2x)+f(3x)+f(4x)+f(5x), where f(x)=sin(x)-cos(x).

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

Offset

1,1

Comments

See A198745 for a guide to related sequences.

Links

Table of n, a(n) for n=1..100.

Index entries for transcendental numbers.

Example

x=6.069500393967011029293576253857045423823...
min=-6.682126364889810370734279330610851580...

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] (* A198751 *)
RealDigits[v] (* A198752 *)
Plot[s[t], {t, -2 Pi, 2 Pi}, PlotRange -> {-7, 4.5}]

Prog

(PARI) solve(x=6, 6.5, 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)) \\ Charles R Greathouse IV, May 17 2026

Crossrefs

Cf. A198745.

Sequence in context: A093577 A065442 A368501 * A141462 A354330 A055955

Adjacent sequences: A198749 A198750 A198751 * A198753 A198754 A198755

Keyword

nonn,cons

Author

Clark Kimberling, Oct 29 2011

Status

approved