A198738 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, 2, 9, 4, 4, 2, 8, 9, 4, 6, 9, 5, 2, 1, 1, 7, 6, 4, 0, 5, 6, 0, 5, 3, 3, 3, 9, 7, 0, 4, 6, 4, 5, 0, 0, 7, 5, 7, 3, 6, 7, 8, 3, 8, 6, 1, 9, 5, 4, 9, 3, 1, 8, 1, 4, 1, 4, 2, 6, 2, 3, 9, 6, 5, 8, 2, 1, 1, 4, 9, 9, 8, 0, 5, 4, 5, 8, 4, 0, 5, 7, 2, 3, 6, 3, 3, 9, 6, 8, 6, 2, 5, 9, 9, 6, 2, 8, 7, 8

Offset

1,1

Comments

See A198735 for a guide to related sequences.

Links

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

Index entries for transcendental numbers.

Example

x=5.2944289469521176405605333970464500...
min=-2.75873119163855400111893535814922666...

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}]

Prog

(PARI) solve(x=5, 6, cos(x)+2*cos(2*x)+3*cos(3*x)-sin(x)-2*sin(2*x)-3*sin(3*x)) \\ Charles R Greathouse IV, Apr 20 2026
(PARI) 2*Pi+2*atan(polrootsreal(x^5 + 7*x^4 - 10*x^3 - 38*x^2 - 11*x + 3)[3]) \\ Charles R Greathouse IV, Apr 20 2026

Crossrefs

Cf. A198735.

Sequence in context: A003671 A318379 A065262 * A051356 A188933 A306648

Adjacent sequences: A198735 A198736 A198737 * A198739 A198740 A198741

Keyword

nonn,cons

Author

Clark Kimberling, Oct 29 2011

Extensions

Name fixed by Charles R Greathouse IV, Apr 20 2026

Status

approved