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

3,2

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).

Links

Table of n, a(n) for n=3..68.

Luca Alexander, about 100000 terms

Formula

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

Example

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

Mathematica

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

Prog

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

Crossrefs

Cf. A328184 (denominators).

Sequence in context: A265341 A358793 A094009 * A349772 A088514 A357275

Adjacent sequences: A328182 A328183 A328184 * A328186 A328187 A328188

Keyword

frac,nonn

Author

Luca Alexander, Oct 06 2019

Status

approved