A146306 a(n) = numerator of (n-6)/(2n).

-5, -1, -1, -1, -1, 0, 1, 1, 1, 1, 5, 1, 7, 2, 3, 5, 11, 1, 13, 7, 5, 4, 17, 3, 19, 5, 7, 11, 23, 2, 25, 13, 9, 7, 29, 5, 31, 8, 11, 17, 35, 3, 37, 19, 13, 10, 41, 7, 43, 11, 15, 23, 47, 4, 49, 25, 17, 13, 53, 9, 55, 14, 19, 29, 59, 5, 61, 31, 21, 16, 65, 11, 67, 17, 23, 35, 71, 6, 73, 37

Offset: 1

Author

Artur Jasinski, Oct 29 2008

Keywords

• sign
• easy

Comments

For denominators see A146307.

General formula:

2*cos(2*Pi/n) = Hypergeometric2F1((n-6)/(2n), (n+6)/(2n), 1/2, 3/4) =

Hypergeometric2F1(a(n)/A146307(n), a(n+12)/A146307(n), 1/2, 3/4).

2*cos(2*Pi/n) is root of polynomial of degree = EulerPhi(n)/2 = A000010(n)/2 = A023022(n).

Records in this sequence are congruent to 1 or 5 mod 6 (see A007310).

First occurrence n in this sequence see A146308.

Examples

			Fractions begin with -5/2, -1, -1/2, -1/4, -1/10, 0, 1/14, 1/8, 1/6, 1/5, 5/22, 1/4, ...
		

Links

• Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,0,0,0,2,0,0,0,0,0,0,0,0,0,0,0,-1).

Crossrefs

Cf. A000010, A007310, A023022, A051724, A146307 (denominators), A146308.

Programs

Mathematica

Table[Numerator[(n - 6)/(2 n)], {n, 1, 100}]

Formula

a(n+5) = A051724(n).

Sum_{k=1..n} a(k) ~ (77/288) * n^2. - Amiram Eldar, Apr 04 2024

From Chai Wah Wu, May 08 2025: (Start)

a(n) = 2*a(n-12) - a(n-24) for n > 24.

G.f.: x*(x^23 + 7*x^22 + 2*x^21 + 3*x^20 + 5*x^19 + 11*x^18 + x^17 + 13*x^16 + 7*x^15 + 5*x^14 + 4*x^13 + 17*x^12 + x^11 + 5*x^10 + x^9 + x^8 + x^7 + x^6 - x^4 - x^3 - x^2 - x - 5)/(x^24 - 2*x^12 + 1). (End)