%I #25 May 22 2022 09:48:39
%S 2,11,23,29,37,43,53,67,71,79,107,109,113,127,137,149,151,163,179,191,
%T 193,197,211,233,239,263,277,281,317,331,337,347,359,373,379,389,401,
%U 421,431,443,449,457,463,487,491,499,541,547,557,569,571,599,613,617,631,641,653,659,673
%N Primes congruent to {1, 2, 4} mod 7.
%C Rational primes that decompose in the field Q(sqrt(-7)). - _N. J. A. Sloane_, Dec 25 2017
%C All these primes can be represented by the binary quadratic form x^2 + xy + 2y^2. - _Alonso del Arte_, Jun 13 2014. Indeed, apart from the fact that 7 is missing, this appears to coincide with A045373. - _N. J. A. Sloane_, Jun 14 2014
%D Şaban Alaca & Kenneth S. Williams, Introductory Algebraic Number Theory. Cambridge: Cambridge University Press (2004) p. 48, Theorem 2.5.4.
%H Vincenzo Librandi, <a href="/A045386/b045386.txt">Table of n, a(n) for n = 1..1000</a>
%H N. J. A. Sloane et al., <a href="https://oeis.org/wiki/Binary_Quadratic_Forms_and_OEIS">Binary Quadratic Forms and OEIS</a> (Index to related sequences, programs, references)
%H <a href="https://oeis.org/index/Pri#primes_decomp_of">Index to sequences related to decomposition of primes in quadratic fields</a>
%t Select[Prime[Range[300]], MemberQ[{1, 2, 4}, Mod[#, 7]] &] (* _Vincenzo Librandi_, Aug 11 2012 *)
%o (Magma) [p: p in PrimesUpTo(600) | p mod 7 in [1, 2, 4]]; // _Vincenzo Librandi_, Aug 11 2012
%Y Cf. A002144, A007645, A045373.
%K nonn,easy
%O 1,1
%A _N. J. A. Sloane_, Dec 11 1999