A207333 Allowed values of degrees of minimal polynomials of 2*cos(Pi/N).

1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 14, 15, 16, 18, 20, 21, 22, 23, 24, 26, 28, 29, 30, 32, 33, 35, 36, 39, 27, 40, 41, 42, 44, 46, 48, 50, 51, 52, 53, 54, 56, 58, 55, 60, 63, 64, 65, 66, 68, 69, 70, 72, 74, 75, 78, 81, 80, 82, 83, 84, 86, 88, 89, 90, 92, 95

Offset

1,2

Comments

The coefficients of the minimal polynomials C(N,x) of the algebraic number 2*cos(Pi/N) are given in A187360, where N is n.

The degree of C(N,x) is delta(N) = 1 if N=1 and delta(N) = phi(2*N)/2 if N > 1, with Euler's totient function phi(n) = A000010(n).

The forbidden degree values are shown in the complement (relative to the positive integers) A079695.

The array of the values N (the indices) for which the degree delta(N) = a(n), n >= 1, is given in A207334.

Links

Table of n, a(n) for n=1..67.

Formula

a(n) gives the allowed degree values, called delta, of the minimal polynomials C ordered increasingly, For C and delta see the comment section.

Example

a(8) = 9 because there is at least one polynomial C(N,x) with degree delta(N)=9. In fact the only N values are 19 and 27.
7 is no member of this sequence (it belongs to the complement A079695).

Crossrefs

Cf. A079695 (complement), A207334 (array of indices of C polynomials with degree a(n)).

Sequence in context: A048265 A288712 A002180 * A179182 A298303 A333635

Adjacent sequences: A207330 A207331 A207332 * A207334 A207335 A207336

Keyword

nonn,easy

Author

Wolfdieter Lang, Feb 19 2012

Status

approved