%I #30 Sep 08 2022 08:44:51

%S 17,53,149,157,281,293,349,353,409,461,509,569,593,613,661,733,797,

%T 829,937,977,1097,1237,1361,1381,1409,1453,1597,1709,1721,1733,1753,

%U 1777,1861,2053,2089,2129,2141

%N Primes of form x^2+17*y^2.

%C Apart from the first term, odd primes p such that (-17/p) = 1 and x^4 - x^2 = 4 has a solution mod p. - _Charles R Greathouse IV_, Nov 11 2012

%C All terms are in {1, 9, 13, 17, 21, 25, 33, 49, 53} mod 68, but this not sufficient for inclusion. - _Charles R Greathouse IV_, Nov 11 2012

%D David A. Cox, "Primes of the Form x^2 + n y^2", Wiley, 1989.

%H Vincenzo Librandi and Ray Chandler, <a href="/A033213/b033213.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)

%t QuadPrimes2[1, 0, 17, 10000] (* see A106856 *)

%o (PARI) is(n)=if(kronecker(17,n)>0 && kronecker(-17,n)>0 && n>2 && isprime(n), kronecker(lift((1+sqrt(Mod(17,n)))/2),n)>0, n==17) \\ _Charles R Greathouse IV_, Nov 11 2012

%o (Magma) /* By first comment: */ [17] cat [p: p in PrimesInInterval(3,2200) | LegendreSymbol(-17, p) eq 1 and exists{x: x in ResidueClassRing(p) | x^4-x^2 eq 4}]; // _Bruno Berselli_, Nov 11 2012

%K nonn,easy

%O 1,1

%A _N. J. A. Sloane_.