cp's OEIS Frontend

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

%I A207334 #10 Oct 02 2013 19:10:22
%S A207334 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,
%T A207334 33,23,26,28,35,36,39,42,45,29,31,32,34,40,48,51,60,37,38,54,57,63,41,
%U A207334 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
%N A207334 Array of indices N for which the minimal polynomial C(N,x) of 2*cos(Pi/N) has allowed degree A207335(n).
%C A207334 For the minimal polynomial C(N,x) and its degree delta(N) see A207333.
%C A207334 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).
%F A207334 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.
%e A207334 Row length l(n), degree values v(n).
%e A207334 l(n):=A207335(n): 3, 3, 2, 4, 1, 4, 5, 2, 3, 1, ...
%e A207334 v(n):=A207333(n): 1, 2, 3, 4, 5, 6, 8, 9, 10, 11, ...
%e A207334 n,  v(n)\m 1  2  3  4  5 ...
%e A207334 1,   1:    1  2  3
%e A207334 2,   2:    4  5  6
%e A207334 3,   3:    7  9
%e A207334 4,   4:    8 10 12 15
%e A207334 5,   5:   11
%e A207334 6,   6:   13 14 18 21
%e A207334 7,   8:   16 17 20 24 30
%e A207334 8,   9:   19 27
%e A207334 9,  10:   22 25 33
%e A207334 10, 11:   23
%e A207334 ...
%e A207334 a(4,2)=10 because C(10,x) has degree A207333(4)=4. In fact, C(10,x) = x^4-5*x^2+5.
%e A207334 The set {N:delta(N)=v(4)=4} = {8,10,12,15} (ordered increasingly). Exactly these N indices lead to degree 4
%e A207334   polynomials C.
%Y A207334 Cf. A032447 (array for cyclotomic polynomials with Euler's phi function as degree).
%K A207334 nonn,easy,tabf
%O A207334 1,2
%A A207334 _Wolfdieter Lang_, Feb 19 2012