A376953 a(n) = least k such that (n*Pi/3)^(2k)/(2 k)! < 1.

1, 1, 2, 4, 5, 6, 8, 9, 11, 12, 13, 15, 16, 18, 19, 20, 22, 23, 25, 26, 27, 29, 30, 32, 33, 35, 36, 37, 39, 40, 42, 43, 44, 46, 47, 49, 50, 52, 53, 54, 56, 57, 59, 60, 61, 63, 64, 66, 67, 69, 70, 71, 73, 74, 76, 77, 78, 80, 81, 83, 84, 86, 87, 88, 90, 91, 93

Offset

0,3

Comments

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

Links

Table of n, a(n) for n=0..66.

Formula

a(n) ~ Pi*exp(1)*n/6 - log(n)/4. - Vaclav Kotesovec, Oct 13 2024

Mathematica

a[n_] := Select[Range[300], (n Pi/3)^(2 #)/(2 #)! < 1 &, 1];
Flatten[Table[a[n], {n, 0, 200}]]

Crossrefs

Cf. A370507, A376952, A376954, A376955, A376956, A376957, A376958, A376959, A376960.

Sequence in context: A000062 A247964 A047317 * A288998 A289026 A289113

Adjacent sequences: A376950 A376951 A376952 * A376954 A376955 A376956

Keyword

nonn

Author

Clark Kimberling, Oct 12 2024

Status

approved