A389816 Numbers k such that sin(k) > 1 - 1/k^2.

1, 2, 8, 33, 51819, 260515, 573204, 4846147, 37362253

Offset

1,2

Links

Table of n, a(n) for n=1..9.

Wikipedia, Dirichlet's approximation theorem

Example

For k=2: sin(2) > 1-1/2^2 so 2 is in the sequence.
For k=3: sin(3) < 1-1/3^2 so 3 is not in the sequence.

Mathematica

q[k_] := Sin[k] > 1 - 1/k^2; Select[Range[300000], q] (* Amiram Eldar, Oct 17 2025 *)

Prog

(PARI) isok(k) = sin(k) > 1 - 1/k^2; \\ Michel Marcus, Oct 17 2025
(Python)
from mpmath import iv
A389816 = [i for i in range(1, 300000) if iv.sin(i) > 1 - 1/iv.mpf(i)**2]  # Jwalin Bhatt, Oct 27 2025

Crossrefs

Subsequence of A046959.

Cf. A070752.

Sequence in context: A191551 A263627 A172448 * A379963 A268601 A026577

Adjacent sequences: A389813 A389814 A389815 * A389817 A389818 A389819

Keyword

nonn,hard,more

Author

Jens Ahlström, Oct 15 2025

Status

approved