A186302 - OEIS

%I #28 Jun 08 2022 03:23:30

%S 3,11,15,23,35,39,51,63,75,83,95,99,111,119,131,135,155,179,183,191,

%T 215,219,231,239,243,251,299,303,315,323,359,363,371,375,411,419,431,

%U 443,455,459,483,491,495,515,519,531,543,551

%N a(n) = ( A007522(n)-1 )/2.

%C From _Wolfdieter Lang_, Oct 24 2013: (Start)

%C Each a(n) is of course congruent 3 (mod 4).

%C a(n) = A055034(p7m8(n)), with p7m8(n) := A007522(n). This is the degree of the minimal polynomial of rho(p7m8(n)):= 2*cos(Pi/p7m8(n)), called C(p7m8(n), x) in A187360. (End)

%H Amiram Eldar, <a href="/A186302/b186302.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = A186303(n)-1.

%e Degree of minimal polynomial C(prime 7 (mod 8), x):

%e n = 2, p7m8(2) = A007522(2) = 23, delta(23) = 11. - _Wolfdieter Lang_, Oct 24 2013

%t (Select[8*Range[200] - 1, PrimeQ] - 1)/2 (* _Amiram Eldar_, Jun 08 2022 *)

%o (PARI) is(n)=n%4==3&&isprime(2*n+1) \\ _Charles R Greathouse IV_, Jan 22 2013

%Y Cf. A007522, A055034, A186303, A187360.

%K nonn,easy

%O 1,1

%A _Marco Matosic_, Feb 17 2011