A375053 a(n) = least k such that (n Pi)^(2 k + 1)/(2 k + 1)! < 1.

1, 3, 7, 11, 16, 20, 24, 28, 33, 37, 41, 45, 50, 54, 58, 62, 67, 71, 75, 79, 84, 88, 92, 96, 101, 105, 109, 113, 118, 122, 126, 131, 135, 139, 143, 148, 152, 156, 160, 165, 169, 173, 177, 182, 186, 190, 194, 199, 203, 207, 212, 216, 220, 224, 229, 233, 237

Offset

0,2

Comments

The numbers (n Pi)^(2 k + 1)/(2 k + 1)! are the coefficients in the Maclaurin series for sin x when x = n*Pi.

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

Links

Table of n, a(n) for n=0..56.

Mathematica

z = 300; r = Pi;
a[n_] := Select[Range[z], (n  r)^(2 # + 1)/(2 # + 1)! < 1 &, 1]
Flatten[Table[a[n], {n, 0, 100}]]

Crossrefs

Cf. A374987, A376456, A376457, A375054, A375057.

Sequence in context: A100900 A117829 A166092 * A184913 A307761 A022821

Adjacent sequences: A375050 A375051 A375052 * A375054 A375055 A375056

Keyword

nonn

Author

Clark Kimberling, Oct 01 2024

Status

approved