A106984 Primes of the form 2x^2 + 11y^2.

2, 11, 13, 19, 29, 43, 61, 83, 101, 107, 109, 131, 139, 149, 173, 197, 211, 227, 277, 283, 293, 307, 347, 349, 373, 461, 491, 523, 541, 547, 557, 563, 571, 613, 659, 677, 701, 733, 739, 787, 811, 821, 827, 853, 877, 941, 997, 1019, 1051, 1069, 1091, 1117

Offset: 1

Author

T. D. Noe, May 09 2005

Keywords

• nonn
• easy

Comments

Discriminant = -88.

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)

Crossrefs

Cf. A139827.

Programs

Magma

[ p: p in PrimesUpTo(2000) | p mod 88 in {2, 11, 13, 19, 21, 29, 35, 43, 51, 61, 83, 85} ]; // Vincenzo Librandi, Jul 23 2012

Mathematica

QuadPrimes2[2, 0, 11, 10000] (* see A106856 *)

PARI

list(lim)=my(v=List([2]),s=[11,13, 19, 21, 29, 35, 43, 51, 61, 83, 85]); forprime(p=11,lim, if(setsearch(s,p%88), listput(v,p))); Vec(v) \\ Charles R Greathouse IV, Feb 09 2017

Formula

The primes are congruent to {2, 11, 13, 19, 21, 29, 35, 43, 51, 61, 83, 85} (mod 88). - T. D. Noe, May 02 2008