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a(n) = (A007521(n)-1)/4.
2

%I #12 Jun 08 2022 03:21:59

%S 1,3,7,9,13,15,25,27,37,39,43,45,49,57,67,69,73,79,87,93,97,99,105,

%T 115,127,135,139,153,163,165,169,175,177,183,189,193,199,205,207,213,

%U 219,235,249,253,255,265,267,273,277,279,295,303,307

%N a(n) = (A007521(n)-1)/4.

%C Because A007521(n) are the primes congruent 5 (mod 8) it is clear that a(n) is congruent 1 (mod 2), that is odd.

%C 2*a(n) = A055034(A007521(n)), the degree of the minimal polynomial C(A007521(n), x) of 2*rho(Pi/A007521(n)) (see A187360).

%H Amiram Eldar, <a href="/A230076/b230076.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = (A007521(n)-1)/4.

%e The minimal polynomial C(A007521(2), x) = C(13, x) has degree 6 = 2*a(2) because C(13, x) = x^6 - x^5 - 5*x^4 + 4*x^3 + 6*x^2 - 3*x -1.

%t (Select[8*Range[0, 200] + 5, PrimeQ] - 1)/4 (* _Amiram Eldar_, Jun 08 2022 *)

%Y Cf. A007521, A055034, A187360, 4*A005123 (1 (mod 8) case), A186287 (3 (mod 8) case), A186302 (7 (mod 8) case).

%K nonn,easy

%O 1,2

%A _Wolfdieter Lang_, Oct 24 2013