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

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

Author

Wolfdieter Lang, Feb 19 2012

Keywords

• nonn
• easy
• tabf

Comments

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).

Examples

			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.
		

Crossrefs

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

Formula

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.