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A198728
Decimal expansion of the least x>0 that gives the absolute minimum of sin(x)+sin(2x)+sin(3x).
1
5, 6, 1, 5, 8, 9, 4, 2, 3, 5, 6, 5, 5, 1, 1, 3, 7, 3, 0, 4, 3, 0, 5, 1, 0, 6, 1, 3, 0, 2, 9, 7, 7, 0, 5, 2, 5, 7, 6, 8, 4, 2, 3, 2, 5, 4, 2, 6, 3, 1, 8, 2, 4, 8, 9, 8, 0, 3, 8, 4, 3, 5, 2, 7, 4, 2, 3, 0, 7, 3, 8, 9, 7, 4, 8, 5, 0, 8, 7, 6, 9, 5, 9, 2, 4, 5, 1, 2, 5, 7, 6, 5, 1, 3, 7, 6, 3, 8, 5
OFFSET
1,1
COMMENTS
See A198677 for a guide to related sequences.
EXAMPLE
x=5.615894235655113730430510613029770525768423...
min=-2.499607604320056604368126285618043218243...
MATHEMATICA
n = 3; f[t_] = Sin[t]; 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] (* A198679 *)
RealDigits[v] (* A198680 *)
Plot[s[t], {t, -3 Pi, 3 Pi}]
(* Second program: *)
RealDigits[3*Pi/2 + ArcSin[Root[-1 - 4x + 2x^2 + 6x^3, 3]], 10, 99] // First (* Jean-François Alcover, Feb 15 2013 *)
CROSSREFS
Cf. A198677.
Sequence in context: A198419 A323738 A222133 * A345144 A238135 A195449
KEYWORD
nonn,cons
AUTHOR
Clark Kimberling, Oct 29 2011
STATUS
approved