A328185 Numerators associated with A328184.

1, 3, 7, 5, 11, 7, 5, 9, 19, 11, 23, 13, 9, 15, 31, 17, 35, 19, 13, 21, 43, 23, 47, 25, 17, 27, 55, 29, 59, 31, 21, 33, 67, 35, 71, 37, 25, 39, 79, 41, 83, 43, 29, 45, 91, 47, 95, 49, 33, 51, 103, 53, 107, 55, 37, 57, 115, 59, 119, 61, 41, 63, 127, 65, 131, 67

Offset: 3

Author

Luca Alexander, Oct 06 2019

Keywords

• frac
• nonn

Comments

Geometric Interpretation: Given n-sided regular polygon "rolling" on a flat surface with constant angular velocity, a(n) is the numerator of the ratio:

[("time" taken for any one vertex to move from highest point to lowest point) / ("time" taken for polygon to finish one complete turn)] := b(n).

Lim_{n->infinity} b(n) = 1/2 (can be easily proven).

Examples

			For n = 3, a(3) = numerator of ((2*3-3)/4*n) = numerator of (3/12) = numerator of (1/4) = 1.
		

Links

• Luca Alexander, about 100000 terms

Crossrefs

Cf. A328184 (denominators).

Programs

Mathematica

Array[Numerator[(2 (# - 1) - Mod[#, 2])/(4 #)] &, 66, 3] (* Michael De Vlieger, Oct 06 2019 *)

PARI

a(n) = {numerator((2*(n-1) - n%2)/(4*n))} \\ Andrew Howroyd, Oct 06 2019

Formula

a(n) = numerator((n - 1) / (2*n)) for even n; a(n) = numerator((2*n - 3) / (4*n)) for odd n.