1,1

Inert rational odd primes in the field Q(sqrt(-2)).

Primes p such that p XOR 5 = p - 5. - Brad Clardy, Jul 22 2012

Terms m in A047566 with A010051(m) = 1. - Reinhard Zumkeller, Dec 29 2012

This sequence gives the primes p which satisfy norm(rho(p)) = - 1 with rho(p) := 2*cos(Pi/p) (the length ratio (smallest diagonal)/side in the regular p-gon). The norm of an algebraic number (over Q) is the product over all zeros of its minimal polynomial. Here norm(rho(p)) = (-1)^delta(p)* C(p, 0), with the degree delta(p) = A055034(p) = (p-1)/2. For p == 5 (mod 8) the norm is C(p, 0) (see a comment on 2*A230076) and for p == 7 (mod 8) the norm is -C(p, 0) (see a comment on A186302). For the primes with norm(rho(p)) = +1 see A033200. - Wolfdieter Lang, Oct 24 2013

H. Hasse, Number Theory, Springer-Verlag, NY, 1980, p. 498.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

a(n) ~ 2n log n. - Charles R Greathouse IV, Feb 24 2023

Select[Prime[Range[200]], MemberQ[{5, 7}, Mod[#, 8]]&] (* Harvey P. Dale, Oct 24 2011 *)

(Haskell)

a003628 n = a003628_list !! (n-1)

a003628_list = filter ((== 1) . a010051) a047566_list

-- Reinhard Zumkeller, Dec 29 2012, Jan 22 2012

(PARI) {a(n) = local( cnt, m ); if( n<1, return( 0 )); while( cnt < n, if( isprime( m++) && kronecker( -2, m )==-1, cnt++ )); m} /* Michael Somos, Aug 14 2012 */

(Magma) [ p: p in PrimesUpTo(600) | p mod 8 in {5, 7}]; // Vincenzo Librandi, Aug 22 2012

Cf. A000040, A039706, A033203 (complement with respect to A000040).

Sequence in context: A216748 A216768 A216750 * A216776 A105874 A105904

Adjacent sequences: A003625 A003626 A003627 * A003629 A003630 A003631

nonn,easy,nice

N. J. A. Sloane, Mira Bernstein

approved