A146308 a(n) is the smallest k such that the numerator of (k-6)/(2k) equals n.

6, 7, 14, 15, 22, 11, 78, 13, 38, 33, 46, 17, 150, 19, 62, 51, 70, 23, 222, 25, 86, 69, 94, 29, 294, 31, 110, 87, 118, 35, 366, 37, 134, 105, 142, 41, 438, 43, 158, 123, 166, 47, 510, 49, 182, 141, 190, 53, 582, 55, 206, 159, 214, 59, 654, 61, 230, 177, 238, 65, 726

Offset

0,1

Comments

a(n) = index of first occurrence n in A146306.

General formula:

2*cos(2*Pi/n) = Hypergeometric2F1((n-6)/(2n), (n+6)/(2n), 1/2, 3/4) = Hypergeometric2F1(A146306(n)/A146307(n), A146306(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).

Links

Robert Israel, Table of n, a(n) for n = 0..10000

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

Formula

From Robert Israel, Aug 05 2019: (Start)

If 6 | n then a(n) = 12*n+6

else if 3 | n then a(n) = 3*n+6

else if 2 | n then a(n) = 2*n+6

else a(n) = n+6.

a(n) = 2*a(n-6) - a(n-12).

G.f.: (6 + 7*x + 14*x^2 + 15*x^3 + 22*x^4 + 11*x^5 + 66*x^6 - x^7 + 10*x^8 + 3*x^9 + 2*x^10 - 5*x^11)/(1 - 2*x^6 + x^12). (End)

Maple

f:= proc(n) if n mod 6 = 0 then 12*n+6 elif n::even then 4*n+6 elif n mod 3 = 0 then 3*n+6 else n+6 fi end proc:
map(f, [$0..100]); # Robert Israel, Aug 05 2019

Mathematica

aa = {}; Do[k = 1; While[Numerator[(k - 6)/(2 k)] != n, k++ ]; AppendTo[aa, k], {n, 0, 100}]; aa

Crossrefs

Cf. A007310, A051724, A146306, A146307, A146309.

Sequence in context: A319487 A283772 A080402 * A047589 A125996 A315836

Adjacent sequences: A146305 A146306 A146307 * A146309 A146310 A146311

Keyword

nonn,look

Author

Artur Jasinski, Oct 29 2008

Status

approved