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A198740
Decimal expansion of the least x>0 that gives the absolute minimum of f(x)+f(2x)+f(3x)+f(4x), where f(x)=sin(x)+cos(x).
3
5, 5, 1, 5, 4, 3, 6, 9, 7, 8, 0, 8, 2, 7, 9, 5, 0, 1, 9, 2, 4, 9, 8, 7, 5, 0, 5, 3, 4, 1, 8, 1, 1, 5, 0, 7, 5, 8, 0, 0, 0, 7, 0, 1, 4, 4, 5, 2, 7, 5, 5, 2, 0, 0, 0, 7, 1, 6, 2, 0, 8, 0, 6, 1, 7, 4, 4, 1, 4, 0, 0, 3, 1, 4, 2, 4, 4, 5, 5, 4, 5, 0, 8, 1, 4, 9, 0, 5, 7, 2, 6, 6, 5, 1, 8, 0, 7, 9, 6
OFFSET
1,1
COMMENTS
See A198735 for a guide to related sequences.
EXAMPLE
x=5.5154369780827950192498750534181150758000...
min=-3.4194065057629463327304557162112432637...
MATHEMATICA
f[t_] := Sin[t] + Cos[t]
n = 4; 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] (* A198739 *)
RealDigits[v] (* A198740 *)
Plot[s[t], {t, -3 Pi, 3 Pi}]
CROSSREFS
Cf. A198735.
Sequence in context: A322545 A256737 A055183 * A082956 A190101 A097566
KEYWORD
nonn,cons
AUTHOR
Clark Kimberling, Oct 29 2011
STATUS
approved