A376952 a(n) = least k such that (n*Pi/2)^(2k)/(2 k)! < 1.

1, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 23, 25, 27, 29, 31, 33, 35, 37, 39, 42, 44, 46, 48, 50, 52, 54, 56, 59, 61, 63, 65, 67, 69, 71, 73, 76, 78, 80, 82, 84, 86, 88, 91, 93, 95, 97, 99, 101, 103, 105, 108, 110, 112, 114, 116, 118, 120, 122, 125, 127, 129

Offset

0,2

Comments

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

Links

Table of n, a(n) for n=0..61.

Formula

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

Mathematica

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

Crossrefs

Cf. A370507, A376953, A376954, A376955, A376956, A376957, A376958, A376959, A376960.

Sequence in context: A054965 A059548 A064720 * A029741 A240171 A221284

Adjacent sequences: A376947 A376948 A376951 * A376953 A376954 A376955

Keyword

nonn,new

Author

Clark Kimberling, Oct 12 2024

Status

approved