A198731 - OEIS

A198731

Decimal expansion of the absolute minimum of sin(x)+sin(2x)+sin(3x)+sin(4x)+sin(5x).

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

(list; constant; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

See A198677 for a guide to related sequences.

LINKS

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

EXAMPLE

x=5.8590231016815427641022649970323299904568...

min=-3.96217336350328560023197791110649098988...

MATHEMATICA

n = 5; 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] (* A198731 *)

RealDigits[v] (* A198732 *)

Plot[s[t], {t, -3 Pi, 3 Pi}]

PROG

(PARI) my(t=solve(x=-1, 0, cos(x)+2*cos(2*x)+3*cos(3*x)+4*cos(4*x)+5*cos(5*x))); sin(t)+sin(2*t)+sin(3*t)+sin(4*t)+sin(5*t) \\ Charles R Greathouse IV, May 17 2026

CROSSREFS

Cf. A198677.

Sequence in context: A337446 A020834 A389032 * A153019 A324994 A201614

Adjacent sequences: A198728 A198729 A198730 * A198732 A198733 A198734

KEYWORD

nonn,cons,changed

AUTHOR

Clark Kimberling, Oct 29 2011

STATUS

approved