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A198742
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).
3
5, 6, 5, 5, 5, 5, 2, 1, 5, 8, 6, 1, 7, 6, 2, 3, 0, 9, 4, 3, 2, 5, 7, 6, 2, 8, 3, 7, 4, 7, 4, 0, 3, 7, 5, 5, 8, 8, 6, 0, 7, 4, 3, 7, 7, 2, 2, 7, 9, 8, 9, 3, 8, 8, 0, 9, 7, 4, 3, 1, 5, 1, 6, 5, 6, 2, 0, 3, 9, 2, 0, 3, 2, 5, 0, 3, 8, 6, 4, 9, 0, 6, 2, 7, 7, 6, 7, 9, 5, 6, 4, 4, 1, 4, 3, 6, 4, 2, 8
OFFSET
1,1
COMMENTS
See A198735 for a guide to related sequences.
EXAMPLE
x=5.655552158617623094325762837474037558860...
min=-4.077697884877698503776497218972682969...
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] (* A198741 *)
RealDigits[v] (* A198742 *)
Plot[s[t], {t, -2 Pi, 2 Pi}, PlotRange -> {-4.1, 7}]
CROSSREFS
Cf. A198735.
Sequence in context: A273065 A071629 A087496 * A106704 A127205 A006944
KEYWORD
nonn,cons
AUTHOR
Clark Kimberling, Oct 29 2011
STATUS
approved