A198754 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).

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

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=-7.9923425075026144580650827802488...

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}]

Crossrefs

Cf. A198745.

Sequence in context: A267479 A285824 A269955 * A243317 A021625 A011221

Adjacent sequences: A198751 A198752 A198753 * A198755 A198756 A198757

Keyword

nonn,cons

Author

Clark Kimberling, Oct 29 2011

Status

approved