cp's OEIS Frontend

A003625 Primes congruent to {3, 5, 6} mod 7.

%I A003625 M2487 #49 Dec 28 2024 00:07:22
%S A003625 3,5,13,17,19,31,41,47,59,61,73,83,89,97,101,103,131,139,157,167,173,
%T A003625 181,199,223,227,229,241,251,257,269,271,283,293,307,311,313,349,353,
%U A003625 367,383,397,409,419,433,439,461,467,479,503,509,521,523,563,577,587,593
%N A003625 Primes congruent to {3, 5, 6} mod 7.
%C A003625 Inert rational primes in Q(sqrt(-7)).
%C A003625 For terms >= 13, sequence consists of primes p such that Sum_{k=0..p} binomial(2*k,k)^3 == 8 (mod p). - _Benoit Cloitre_, Aug 10 2003
%C A003625 Primes which cannot be written in the form a^2 + 7*b^2, where a >= 0, b >= 0. - _V. Raman_, Sep 08 2012
%C A003625 Conjecture: Also such primes p where the polynomial x^2 + x + 2 is irreducible over GF(p). - _Federico Provvedi_, Jul 21 2018
%C A003625 Primes that have -7 as a quadratic nonresidue, or equivalently, primes that are quadratic nonresidues modulo 7. - _Jianing Song_, Jul 21 2018
%D A003625 H. Hasse, Number Theory, Springer-Verlag, NY, 1980, p. 498.
%D A003625 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A003625 Vincenzo Librandi, <a href="/A003625/b003625.txt">Table of n, a(n) for n = 1..1000</a>
%H A003625 <a href="https://oeis.org/index/Pri#primes_decomp_of">Index to sequences related to decomposition of primes in quadratic fields</a>
%t A003625 Select[Prime[Range[800]],MemberQ[{3, 5, 6},Mod[#,7]]&] (* _Vincenzo Librandi_, Aug 04 2012 *)
%o A003625 (Magma) [p: p in PrimesUpTo(1000) | p mod 7 in [3, 5, 6]]; // _Vincenzo Librandi_, Aug 04 2012
%o A003625 (PARI)  {a(n) = local( cnt, m ); if( n<1, return( 0 )); while( cnt < n, if( isprime( m++) && kronecker( -7, m )==-1, cnt++ )); m} /* _Michael Somos_, Aug 14 2012 */
%K A003625 nonn
%O A003625 1,1
%A A003625 _N. J. A. Sloane_, _Mira Bernstein_