cp's OEIS Frontend

A139886 Primes of the form 10x^2 + 19y^2.

%I A139886 #33 Oct 19 2024 01:58:42
%S A139886 19,29,59,109,179,181,211,269,331,379,421,509,659,661,811,829,941,971,
%T A139886 1019,1021,1091,1171,1181,1229,1291,1381,1459,1549,1571,1579,1699,
%U A139886 1709,1741,1789,1861,1931,1979,2029,2131,2141,2179,2269,2309,2339
%N A139886 Primes of the form 10x^2 + 19y^2.
%C A139886 Discriminant = -760. See A139827 for more information.
%C A139886 10*x^2 + 19 produces 19 consecutive primes belonging to A028416 for x from 0 to 18. - _Davide Rotondo_, Jun 13 2022
%C A139886 Primes p such that Kronecker(2,p) <= 0, Kronecker(5,p) >= 0 and Kronecker(-19,p) <= 0. - _Jianing Song_, Jun 13 2022
%H A139886 Vincenzo Librandi and Ray Chandler, <a href="/A139886/b139886.txt">Table of n, a(n) for n = 1..10000</a> [First 1000 terms from Vincenzo Librandi]
%H A139886 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)
%F A139886 The primes are congruent to {19, 21, 29, 51, 59, 69, 91, 109, 141, 179, 181, 189, 211, 219, 221, 259, 261, 269, 299, 331, 341, 371, 379, 411, 421, 451, 459, 469, 509, 531, 611, 621, 629, 659, 661, 699, 749} (mod 760). [For the other direction, primes satisfying this congruence are terms of this sequence since 760 is a term in A003171. - _Jianing Song_, Jun 13 2022]
%t A139886 QuadPrimes2[10, 0, 19, 10000] (* see A106856 *)
%o A139886 (Magma) [ p: p in PrimesUpTo(3000) | p mod 760 in {19, 21, 29, 51, 59, 69, 91, 109, 141, 179, 181, 189, 211, 219, 221, 259, 261, 269, 299, 331, 341, 371, 379, 411, 421, 451, 459, 469, 509, 531, 611, 621, 629, 659, 661, 699, 749}]; // _Vincenzo Librandi_, Jul 30 2012
%Y A139886 Apart from 19, intersection of A003629, A045468 and A191063.
%K A139886 nonn,easy
%O A139886 1,1
%A A139886 _T. D. Noe_, May 02 2008