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A139886
Primes of the form 10x^2 + 19y^2.
2
19, 29, 59, 109, 179, 181, 211, 269, 331, 379, 421, 509, 659, 661, 811, 829, 941, 971, 1019, 1021, 1091, 1171, 1181, 1229, 1291, 1381, 1459, 1549, 1571, 1579, 1699, 1709, 1741, 1789, 1861, 1931, 1979, 2029, 2131, 2141, 2179, 2269, 2309, 2339
OFFSET
1,1
COMMENTS
Discriminant = -760. See A139827 for more information.
10*x^2 + 19 produces 19 consecutive primes belonging to A028416 for x from 0 to 18. - Davide Rotondo, Jun 13 2022
Primes p such that Kronecker(2,p) <= 0, Kronecker(5,p) >= 0 and Kronecker(-19,p) <= 0. - Jianing Song, Jun 13 2022
LINKS
Vincenzo Librandi and Ray Chandler, Table of n, a(n) for n = 1..10000 [First 1000 terms from Vincenzo Librandi]
N. J. A. Sloane et al., Binary Quadratic Forms and OEIS (Index to related sequences, programs, references)
FORMULA
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]
MATHEMATICA
QuadPrimes2[10, 0, 19, 10000] (* see A106856 *)
PROG
(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
CROSSREFS
Apart from 19, intersection of A003629, A045468 and A191063.
Sequence in context: A136071 A088998 A181606 * A089724 A265804 A276732
KEYWORD
nonn,easy,changed
AUTHOR
T. D. Noe, May 02 2008
STATUS
approved