A198748 Decimal expansion of the least x>0 that gives the absolute minimum of f(x)+f(2x)+f(3x), where f(x)=sin(x)-cos(x).

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

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}]

Crossrefs

Cf. A198745.

Sequence in context: A272610 A350760 A340216 * A196754 A198217 A021631

Adjacent sequences: A198745 A198746 A198747 * A198749 A198750 A198751

Keyword

nonn,cons

Author

Clark Kimberling, Oct 29 2011

Status

approved