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A207334
Array of indices N for which the minimal polynomial C(N,x) of 2*cos(Pi/N) has allowed degree A207335(n).
2
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).
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: A372656 A375184 A367935 * A294660 A180198 A180199
KEYWORD
nonn,easy,tabf
AUTHOR
Wolfdieter Lang, Feb 19 2012
STATUS
approved