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A146307
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a(n) = denominator of (n-6)/(2n) = denominator of (n+6)/(2n).
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5
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2, 1, 2, 4, 10, 1, 14, 8, 6, 5, 22, 4, 26, 7, 10, 16, 34, 3, 38, 20, 14, 11, 46, 8, 50, 13, 18, 28, 58, 5, 62, 32, 22, 17, 70, 12, 74, 19, 26, 40, 82, 7, 86, 44, 30, 23, 94, 16, 98, 25, 34, 52, 106, 9, 110, 56, 38, 29, 118, 20, 122, 31, 42, 64, 130, 11, 134, 68, 46, 35, 142, 24
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OFFSET
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1,1
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COMMENTS
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General formula:
2*cos(2*Pi/n) = Hypergeometric2F1((n-6)/(2n), (n+6)/(2n), 1/2, 3/4) =
2*cos(2*Pi/n) is a root of a polynomial of degree EulerPhi(n)/2 = A000010(n)/2 = A023022(n).
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.
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
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LINKS
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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).
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MAPLE
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f:= n -> denom((n-6)/(2*n)):
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MATHEMATICA
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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 *)
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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