This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A038883 #62 Feb 17 2022 20:34:25
%S A038883 3,13,17,23,29,43,53,61,79,101,103,107,113,127,131,139,157,173,179,
%T A038883 181,191,199,211,233,251,257,263,269,277,283,311,313,337,347,367,373,
%U A038883 389,419,433,439,443,467,491,503,521,523,547,563,569,571,599,601,607,641
%N A038883 Odd 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
%C A038883 Primes p such that x^2 + x = 3 has a solution mod p (the solutions over the reals are (-1+-sqrt(13))/2). - _Joerg Arndt_, Jul 27 2011
%D A038883 Z. I. Borevich and I. R. Shafarevich, Number Theory.
%H A038883 Vincenzo Librandi, <a href="/A038883/b038883.txt">Table of n, a(n) for n = 1..1000</a>
%H A038883 Peter Luschny, <a href="/wiki/User:Peter_Luschny/BinaryQuadraticForms#Implementation">Binary Quadratic Forms</a>
%H A038883 N. J. A. Sloane et al., <a href="/wiki/Binary_Quadratic_Forms_and_OEIS">Binary Quadratic Forms and OEIS</a> (Index to related sequences, programs, references)
%H A038883 D. B. Zagier, <a href="https://doi.org/10.1007/978-3-642-61829-1">Zetafunktionen und quadratische Körper</a>, Springer, 1981.
%F A038883 A000040 \ A120330 U {13}: Complement of A120330 in the primes, and 13. - _M. F. Hasler_, Feb 17 2022
%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 Select[ Prime@ Range@ 118, JacobiSymbol[ #, 13] > -1 &] (* _Robert G. Wilson v_, May 16 2008 *)
%t A038883 Select[Flatten[Table[13n + {1, 3, 4, 9, 10, 12}, {n, 50}]], PrimeQ[#] &] (* _Alonso del Arte_, Sep 16 2012 *)
%o A038883 (PARI) forprime(p=3,1e3,if(issquare(Mod(13,p)),print1(p", "))) \\ _Charles R Greathouse IV_, Jul 15 2011
%o A038883 (PARI) select( {is_A038883(n)=bittest(5659,n%13)&&isprime(n)}, [0..666]) \\ _M. F. Hasler_, Feb 17 2022
%o A038883 (Sage) # uses[binaryQF]
%o A038883 # The function binaryQF is defined in the link 'Binary Quadratic Forms'.
%o A038883 Q = binaryQF([1, 3, -1])
%o A038883 print(Q.represented_positives(641, 'prime')) # _Peter Luschny_, Sep 20 2018
%Y A038883 Cf. A038872 (d=5). A038873 (d=8). A068228, A141123 (d=12). A038883 (primes p such that d=13 is a square mod p). A038889 (d=17). A141111, A141112 (d=65).
%Y A038883 Cf. A296937.
%Y A038883 CF. A000040, A120330.
%Y A038883 For a list of sequences giving numbers and/or primes represented by binary quadratic forms, see the "Binary Quadratic Forms and OEIS" link.
%K A038883 nonn
%O A038883 1,1
%A A038883 _N. J. A. Sloane_
%E A038883 Edited by _N. J. A. Sloane_, Apr 27 2008, Jul 28 2008