A207334 -id:A207334 - cp's OEIS frontend

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

Wolfdieter Lang, Feb 19 2012

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.

			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).

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

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

A207335 Number of minimal polynomials of 2*cos(Pi/N) with allowed degree given by A207333.

Original entry on oeis.org

3, 3, 2, 4, 1, 4, 5, 2, 3, 1, 7, 1, 1, 6, 5, 6, 2, 2, 1, 9, 1, 1, 2, 1, 5, 7, 1, 1, 11, 1, 8, 1, 4, 4, 2, 13, 2, 1, 2, 1, 5, 1, 4, 2, 11, 1, 8, 1, 4, 1, 1, 2, 16, 1, 1, 4, 10

Offset: 1

Wolfdieter Lang, Feb 19 2012

For the minimal polynomials C(N,x) of 2*cos(Pi/N) with degree delta(N) see A207333.

			a(8)=2 because there are exactly 2 values of N, namely 19 and 27 (see row no. 7 of the array A207334), for which the minimal polynomial C(N,x) has degree delta(N) = A207333(8) = 9.

Cf. A207333, A143422.

a(n) is the number of different indices N of minimal polynomials C(N,x) of 2*cos(Pi/N) with allowed degree delta(N)=A207333(n), n>=1.

cp's OEIS Frontend

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

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