A117672 Numbers k such that |cos(k)*cos(k+2)| < (cos(k+1))^2.

2, 3, 5, 6, 8, 9, 11, 12, 14, 15, 17, 18, 21, 24, 25, 27, 28, 30, 31, 33, 34, 36, 37, 39, 40, 43, 46, 47, 49, 50, 52, 53, 55, 56, 58, 59, 61, 62, 65, 68, 69, 71, 72, 74, 75, 77, 78, 80, 81, 83, 84, 87, 90, 91, 93, 94, 96, 97, 99, 100, 102, 103, 105, 106, 109, 112, 113, 115

Offset

1,1

Comments

What is the density of the sequence? I am convinced that this sequence has the same density as A026313.

Links

Chris R. Rehmann, Table of n, a(n) for n = 1..10000

Example

|cos(5)*cos(7)| < (cos(6))^2, therefore 5 is in the sequence.

Mathematica

Select[Range[120], Abs[Cos[ # ]*Cos[ # + 2]] < Cos[ # + 1]^2 &]

Prog

(MATLAB) kmax = 16825; k = 0:kmax; a = k(abs(cos(k).*cos(k+2))<cos(k+1).^2); % Chris R. Rehmann, Feb 21 2026

Crossrefs

Cf. A026313 [same definition with sin instead of cos].

Sequence in context: A052490 A332076 A248562 * A194383 A380383 A186326

Adjacent sequences: A117669 A117670 A117671 * A117673 A117674 A117675

Keyword

nonn

Author

Stefan Steinerberger, Apr 12 2006

Extensions

Offset corrected by Sean A. Irvine, Sep 25 2019

Status

approved