A376954 a(n) = least k such that (2n*Pi/3)^(2k)/(2 k)! < 1.

1, 2, 5, 8, 11, 13, 16, 19, 22, 25, 27, 30, 33, 36, 39, 42, 44, 47, 50, 53, 56, 59, 61, 64, 67, 70, 73, 76, 78, 81, 84, 87, 90, 93, 95, 98, 101, 104, 107, 110, 113, 115, 118, 121, 124, 127, 130, 132, 135, 138, 141, 144, 147, 149, 152, 155, 158, 161, 164, 167

Offset: 0

Author

Clark Kimberling, Oct 12 2024

Keywords

• nonn

Comments

The numbers (2n*Pi/3)^(2k)/(2 k)! are the coefficients in the Maclaurin series for cos x when x = 2n*Pi/3. If m>a(n), then (2m*Pi/3)^(2k)/(2 k)! < 1. A375057 is a trisection of this sequence.

Crossrefs

Cf. A370507, A376952, A376953, A376955, A376956, A376957, A376958, A376959, A376960.

Programs

Mathematica

a[n_] := Select[Range[200], (2n Pi/3)^(2 #)/(2 #)! < 1 &, 1];
Flatten[Table[a[n], {n, 0, 200}]]

Formula

a(n) ~ Pi*exp(1)*n/3 - log(n)/4. - Vaclav Kotesovec, Oct 13 2024