A198737 Decimal expansion of the absolute minimum of f(x)+f(2x)+f(3x), where f(x)=sin(x)+cos(x).

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

Offset

1,1

Comments

See A198735 for a guide to related sequences.

Links

Table of n, a(n) for n=1..99.

Example

x=5.2944289469521176405605333970464500...
min=-2.7587311916385540011189353581492...

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]  (* A198737 *)
RealDigits[v]  (* A198738 *)
Plot[s[t], {t, -3 Pi, 3 Pi}]
RealDigits[Abs[NMinimize[Sin[x]+Cos[x]+Sin[2x]+Cos[2x]+Sin[3x]+Cos[3x], x, WorkingPrecision-> 100][[1]]], 10, 100][[1]] (* Harvey P. Dale, Mar 27 2022 *)

Crossrefs

Cf. A198735.

Sequence in context: A181320 A195450 A079833 * A010593 A332322 A117931

Adjacent sequences: A198734 A198735 A198736 * A198738 A198739 A198740

Keyword

nonn,cons

Author

Clark Kimberling, Oct 29 2011

Status

approved