A139852 Primes of the form 7x^2 + 16y^2.

7, 23, 71, 79, 127, 151, 191, 239, 263, 359, 431, 463, 487, 599, 631, 743, 751, 823, 863, 911, 919, 967, 991, 1031, 1087, 1103, 1303, 1327, 1367, 1423, 1439, 1471, 1583, 1607, 1663, 1759, 1831, 1871, 1999, 2039, 2087, 2111, 2143, 2207, 2311

Offset

1,1

Comments

Discriminant=-448. See A139827 for more information.

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

Except for 7, the primes are congruent to {15, 23, 39} (mod 56).

Mathematica

QuadPrimes2[7, 0, 16, 10000] (* see A106856 *)

Prog

(Magma) [7] cat [ p: p in PrimesUpTo(3000) | p mod 56 in {15, 23, 39}]; // Vincenzo Librandi, Jul 29 2012
(PARI) list(lim)=my(v=List(), w, t); for(x=1, sqrtint(lim\7), w=7*x^2; for(y=0, sqrtint((lim-w)\16), if(isprime(t=w+16*y^2), listput(v, t)))); Set(v) \\ Charles R Greathouse IV, Feb 22 2017

Crossrefs

Sequence in context: A048458 A134350 A005342 * A141194 A198644 A045535

Adjacent sequences: A139849 A139850 A139851 * A139853 A139854 A139855

Keyword

nonn,easy

Author

T. D. Noe, May 02 2008

Status

approved