

A106904


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


5



13, 19, 43, 67, 103, 127, 151, 157, 223, 229, 271, 307, 331, 349, 373, 409, 421, 433, 457, 463, 523, 577, 613, 631, 661, 727, 733, 739, 757, 769, 829, 859, 883, 919, 937, 967, 1021, 1033, 1039, 1063, 1069, 1087, 1123, 1171, 1237, 1249, 1279, 1291, 1327
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OFFSET

1,1


COMMENTS

Discriminant=51.
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


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)


MATHEMATICA

QuadPrimes2[1, 1, 13, 10000] (* see A106856 *)


PROG

(PARI) select(p>issquare(Mod(p, 51))&&isprime(p), [1..1500]) \\ See A106903 for alternative code.  M. F. Hasler, Jan 15 2016


CROSSREFS

Sequence in context: A124199 A119869 A272200 * A106903 A098413 A174152
Adjacent sequences: A106901 A106902 A106903 * A106905 A106906 A106907


KEYWORD

nonn,easy


AUTHOR

T. D. Noe, May 09 2005


STATUS

approved



