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A146306
a(n) = numerator of (n-6)/(2n).
4
-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
1,1
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.
FORMULA
a(n+5) = A051724(n).
Sum_{k=1..n} a(k) ~ (77/288) * n^2. - Amiram Eldar, Apr 04 2024
EXAMPLE
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, ...
MATHEMATICA
Table[Numerator[(n - 6)/(2 n)], {n, 1, 100}]
CROSSREFS
Cf. A000010, A007310, A023022, A051724, A146307 (denominators), A146308.
Sequence in context: A162298 A196755 A199510 * A336697 A326073 A365490
KEYWORD
sign,easy
AUTHOR
Artur Jasinski, Oct 29 2008
STATUS
approved