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

1,2

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).

Links

Table of n, a(n) for n=1..78.

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.

Example

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).

Sequence in context: A356759 A372656 A367935 * A294660 A180198 A180199

Adjacent sequences: A207331 A207332 A207333 * A207335 A207336 A207337

Keyword

nonn,easy,tabf

Author

Wolfdieter Lang, Feb 19 2012

Status

approved