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

%I #24 Sep 08 2022 08:45:18

%S 2,11,13,19,29,43,61,83,101,107,109,131,139,149,173,197,211,227,277,

%T 283,293,307,347,349,373,461,491,523,541,547,557,563,571,613,659,677,

%U 701,733,739,787,811,821,827,853,877,941,997,1019,1051,1069,1091,1117

%N Primes of the form 2x^2 + 11y^2.

%C Discriminant = -88.

%H Vincenzo Librandi and Ray Chandler, <a href="/A106984/b106984.txt">Table of n, a(n) for n = 1..10000</a> [First 1000 terms from Vincenzo Librandi]

%H 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 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

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

%o (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

%o (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

%Y Cf. A139827.

%K nonn,easy

%O 1,1

%A _T. D. Noe_, May 09 2005

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Last modified April 26 16:30 EDT 2024. Contains 372003 sequences. (Running on oeis4.)