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%I #16 Apr 04 2024 07:54:25
%S -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,
%T 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,
%U 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
%N a(n) = numerator of (n-6)/(2n).
%C For denominators see A146307.
%C General formula:
%C 2*cos(2*Pi/n) = Hypergeometric2F1((n-6)/(2n), (n+6)/(2n), 1/2, 3/4) =
%C Hypergeometric2F1(a(n)/A146307(n), a(n+12)/A146307(n), 1/2, 3/4).
%C 2*cos(2*Pi/n) is root of polynomial of degree = EulerPhi(n)/2 = A000010(n)/2 = A023022(n).
%C Records in this sequence are congruent to 1 or 5 mod 6 (see A007310).
%C First occurrence n in this sequence see A146308.
%F a(n+5) = A051724(n).
%F Sum_{k=1..n} a(k) ~ (77/288) * n^2. - _Amiram Eldar_, Apr 04 2024
%e 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, ...
%t Table[Numerator[(n - 6)/(2 n)], {n, 1, 100}]
%Y Cf. A000010, A007310, A023022, A051724, A146307 (denominators), A146308.
%K sign,easy
%O 1,1
%A _Artur Jasinski_, Oct 29 2008
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