A207333 -id:A207333 - cp's OEIS frontend

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

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.

A207334 Array of indices N for which the minimal polynomial C(N,x) of 2*cos(Pi/N) has allowed degree A207335(n).

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 9, 8, 10, 12, 15, 11, 13, 14, 18, 21, 16, 17, 20, 24, 30, 19, 27, 22, 25, 33, 23, 26, 28, 35, 36, 39, 42, 45, 29, 31, 32, 34, 40, 48, 51, 60, 37, 38, 54, 57, 63, 41, 44, 50, 55, 66, 75, 43, 49, 46, 69, 47, 52, 56, 65, 70, 72, 78, 84, 90, 105, 53, 81, 58, 87, 59, 61, 62, 77, 93, 99

Offset: 1

Wolfdieter Lang, Feb 19 2012

For the minimal polynomial C(N,x) and its degree delta(N) see A207333.

The row length sequence l(n) of this array is A207335(n). The allowed values for the degree delta(N) are v(n):=A207333(n).

			Row length l(n), degree values v(n).
l(n):=A207335(n): 3, 3, 2, 4, 1, 4, 5, 2, 3, 1, ...
v(n):=A207333(n): 1, 2, 3, 4, 5, 6, 8, 9, 10, 11, ...
n,  v(n)\m 1  2  3  4  5 ...
1,   1:    1  2  3
2,   2:    4  5  6
3,   3:    7  9
4,   4:    8 10 12 15
5,   5:   11
6,   6:   13 14 18 21
7,   8:   16 17 20 24 30
8,   9:   19 27
9,  10:   22 25 33
10, 11:   23
...
a(4,2)=10 because C(10,x) has degree A207333(4)=4. In fact, C(10,x) = x^4-5*x^2+5.
The set {N:delta(N)=v(4)=4} = {8,10,12,15} (ordered increasingly). Exactly these N indices lead to degree 4
  polynomials C.

Cf. A032447 (array for cyclotomic polynomials with Euler's phi function as degree).

a(n,m), m=1..l(n):=A207335(n), n>=1, gives the m-th member of the set {N positive integer: delta(N)= v(n):= A207333(n)}, when read as ordered list with increasing numbers.

cp's OEIS Frontend

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

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