OFFSET
1,1
COMMENTS
For numerators see A146306.
General formula:
2*cos(2*Pi/n) = Hypergeometric2F1((n-6)/(2n), (n+6)/(2n), 1/2, 3/4) =
Records in this sequence are even and are congruent to 2 or 10 mod 12 (see A091999).
Indices where odd numbers occur in this sequence are 4n-2 (see A016825).
Indices where prime numbers occur in this sequence see A146309.
From Robert Israel, Apr 21 2021: (Start)
a(n) = 2*n if n == 1, 5, 7 or 11 (mod 12).
a(n) = n if n == 4 or 8 (mod 12).
a(n) = 2*n/3 if n == 3 or 9 (mod 12).
a(n) = n/2 if n == 2 or 10 (mod 12).
a(n) = n/3 if n == 0 (mod 12).
a(n) = n/6 if n == 6 (mod 12). (End)
Sum_{k=1..n} a(k) ~ (77/144) * n^2. - Amiram Eldar, Apr 04 2024
LINKS
Robert Israel, Table of n, a(n) for n = 1..10000
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).
MAPLE
f:= n -> denom((n-6)/(2*n)):
map(f, [$1..100]); # Robert Israel, Apr 20 2021
MATHEMATICA
Table[Denominator[(n - 6)/(2 n)], {n, 1, 100}]
LinearRecurrence[{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1}, {2, 1, 2, 4, 10, 1, 14, 8, 6, 5, 22, 4, 26, 7, 10, 16, 34, 3, 38, 20, 14, 11, 46, 8}, 80] (* Harvey P. Dale, May 15 2022 *)
CROSSREFS
KEYWORD
AUTHOR
Artur Jasinski, Oct 29 2008
STATUS
approved