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 A106904 Primes of the form x^2-xy+13y^2, with x and y nonnegative. 5

%I

%S 13,19,43,67,103,127,151,157,223,229,271,307,331,349,373,409,421,433,

%T 457,463,523,577,613,631,661,727,733,739,757,769,829,859,883,919,937,

%U 967,1021,1033,1039,1063,1069,1087,1123,1171,1237,1249,1279,1291,1327

%N Primes of the form x^2-xy+13y^2, with x and y nonnegative.

%C Discriminant=-51.

%C Also: Primes which are squares (mod 51). Differs from the subsequence A106903 (because x^2+xy+y^2 = (x+y)^2 - (x+y)y + y^2) from a(20) = 463 on, A106903(20) = 523. Terms which are not in A106903 are: 463, 631, 1033, 1039, 1279, 1291,... Up to 1279 these are also in A139643. Cf. also A191034. - _M. F. Hasler_, Jan 15 2016

%H Vincenzo Librandi and Ray Chandler, <a href="/A106904/b106904.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, -1, 13, 10000] (* see A106856 *)

%o (PARI) select(p->issquare(Mod(p,51))&&isprime(p),[1..1500]) \\ See A106903 for alternative code. - _M. F. Hasler_, Jan 15 2016

%K nonn,easy

%O 1,1

%A _T. D. Noe_, May 09 2005

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Last modified January 25 01:49 EST 2020. Contains 331229 sequences. (Running on oeis4.)