A375057 a(n) = least k such that (n*pi)^(2k)/(2 k)! < 1.

1, 4, 8, 12, 16, 20, 25, 29, 33, 37, 42, 46, 50, 54, 59, 63, 67, 71, 76, 80, 84, 88, 93, 97, 101, 105, 110, 114, 118, 122, 127, 131, 135, 140, 144, 148, 152, 157, 161, 165, 169, 174, 178, 182, 186, 191, 195, 199, 203, 208, 212, 216, 221, 225, 229, 233, 238

Offset: 0

Author

Clark Kimberling, Oct 01 2024

Keywords

• nonn

Comments

The numbers (n*Pi)^(2k)/(2 k)! are the coefficients in the Maclaurin series for cos x when x = n*Pi.

(n*pi)^k/(2 k)! < 1 for every k >= a(n).

Crossrefs

Cf. A374987, A376456, A376457, A375053, A375054.

Programs

Mathematica

a[n_] := Select[Range[300], (n Pi)^(2 #)/(2 #)! < 1 &, 1]
Flatten[Table[a[n], {n, 0, 300}]]

Extensions

Edited by Clark Kimberling, Oct 10 2024