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A106863 Primes of the form x^2+xy+5y^2. 7

%I #22 Dec 25 2017 20:11:13

%S 5,7,11,17,19,23,43,47,61,73,83,101,131,137,139,149,157,163,191,197,

%T 199,229,233,239,251,263,271,277,283,311,313,347,349,353,359,367,389,

%U 397,419,443,457,461,463,467,479,491,499,503,541,557,571,577,587,593

%N Primes of the form x^2+xy+5y^2.

%C Discriminant=-19.

%C Also, primes of the form x^2-xy+5y^2 with x and y nonnegative.

%C Also, primes which are a square (mod 19) (or, (mod 38) - cf. A191028). - _M. F. Hasler_, Jan 15 2016

%C Also, primes p such that Legendre(-2,p) = 0 or 1. - _N. J. A. Sloane_, Dec 25 2017

%H Vincenzo Librandi and Ray Chandler, <a href="/A106863/b106863.txt">Table of n, a(n) for n = 1..10000</a> [First 5000 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)

%t QuadPrimes2[1, -1, 5, 10000] (* see A106856 *)

%o (PARI) select(p->issquare(Mod(p, 19))&&isprime(p), [1..1000]) \\ _M. F. Hasler_, Jan 15 2016

%Y Primes in A035243.

%K nonn,easy

%O 1,1

%A _T. D. Noe_, May 09 2005

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Last modified March 29 08:59 EDT 2024. Contains 371268 sequences. (Running on oeis4.)