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

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}]

Crossrefs

Cf. A198735.

Sequence in context: A226021 A242059 A178668 * A201944 A165242 A104542

Adjacent sequences: A198741 A198742 A198743 * A198745 A198746 A198747

Keyword

nonn,cons

Author

Clark Kimberling, Oct 29 2011

Status

approved