A198733 - OEIS

A198733

Decimal expansion of the absolute minimum of sin(x)+sin(2x)+sin(3x)+sin(4x)+sin(5x)+sin(6x).

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

(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..106.

EXAMPLE

x=5.924356380456046882352862563376763567376562...

min=-4.690361803953941719169567767677307460891...

MATHEMATICA

n = 6; 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] (* A198733 *)

RealDigits[v] (* A198734 *)

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

RealDigits[FindMinimum[Plus@@Table[Sin[n*x], {n, 6}], {x, .1}, WorkingPrecision -> 100][[1]]][[1]] (* Harvey P. Dale, Dec 08 2015 *)

PROG

(PARI) my(t=solve(x=18, 19, cos(x)+cos(2*x)*2+cos(3*x)*3+cos(4*x)*4+cos(5*x)*5+cos(6*x)*6)); sin(t)+sin(2*t)+sin(3*t)+sin(4*t)+sin(5*t)+sin(6*t) \\ Charles R Greathouse IV, May 15 2026

CROSSREFS

Cf. A198677.

Sequence in context: A210665 A228586 A200107 * A010478 A106146 A154521

Adjacent sequences: A198730 A198731 A198732 * A198734 A198735 A198736

KEYWORD

nonn,cons,changed

AUTHOR

Clark Kimberling, Oct 29 2011

STATUS

approved