Search: id:A038883
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%I A038883
%S A038883 3,13,17,23,29,43,53,61,79,101,103,107,113,127,131,139,157,173,179,181,
%T A038883 191,199,211,233,251,257,263,269,277,283,311,313,337,347,367,373,389,
%U A038883 419,433,439,443,467,491,503,521,523,547,563,569,571,599,601,607,641
%N A038883 Primes p such that 13 is a square mod p.
%C A038883 Equivalently, by quadratic reciprocity (since 13 == 1 mod 4), primes 
               p which are squares mod 13.
%C A038883 The squares mod 13 are 0, 1, 4, 9, 3, 12 and 10.
%C A038883 Also primes of the form x^2+3*x*y-y^2. Discriminant = 13. Class = 1. 
               This was originally a separate entry, submitted by Laura Caballero 
               Fernandez, Lourdes Calvo Moguer, Maria Josefa Cano Marquez, Oscar 
               Jesus Falcon Ganfornina and Sergio Garrido Morales (oscfalgan(AT)yahoo.es), 
               Jun 06 2008. R. J. Mathar proved that this coincides with the present 
               sequence, Jul 22 2008
%D A038883 Borevich and Shafaewich, Number Theory.
%D A038883 D. B. Zagier, Zetafunktionen und quadratische Koerper.
%e A038883 13 == 1 mod 3 and 1 is a square, so 3 is on the list.
%e A038883 101 is prime and congruent to 7^2 = 49 == 10 (mod 13), so 101 is on the 
               list.
%t A038883 For[a = 1, a < 1001, a++, p = Prime[a]; t = Mod[p, 13]; If[Or[t == 1, 
               t == 3, t == 4, t == 9, t == 10, t == 12], Print[p]]] - N. Fernandez 
               (primeness(AT)borve.org), Jun 22 2006
%t A038883 Select[ Prime@ Range@ 118, JacobiSymbol[ #, 13] > -1 &] (* Robert G. 
               Wilson v, (rgwv(AT)rgwv.com), May 16 2008 *)
%Y A038883 Cf. A038883 (Primes p such that 13 is a square mod p) A141111, A141112 
               (d=65).
%Y A038883 Sequence in context: A119889 A038956 A040123 this_sequence A141188 A019347 
               A045433
%Y A038883 Adjacent sequences: A038880 A038881 A038882 this_sequence A038884 A038885 
               A038886
%K A038883 nonn
%O A038883 1,1
%A A038883 N. J. A. Sloane (njas(AT)research.att.com).
%E A038883 Edited by N. J. A. Sloane (njas(AT)research.att.com), Apr 27 2008, Jul 
               28 2008

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