A106903 - OEIS

A106903

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

13, 19, 43, 67, 103, 127, 151, 157, 223, 229, 271, 307, 331, 349, 373, 409, 421, 433, 457, 523, 577, 613, 661, 727, 733, 739, 757, 769, 829, 859, 883, 919, 937, 967, 1021, 1063, 1069, 1087, 1123, 1171, 1237, 1249, 1327, 1381, 1429, 1447, 1453, 1471

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OFFSET

1,1

COMMENTS

Discriminant=-51.

Differs from A106904 from a(20) = 523 on, A106904(20) = 463. Since x^2 + xy + y^2 = (x+y)^2 - (x+y)y + y^2, this sequence is a subsequence of A106904. - 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->isprime(p)&&(t=qfbsolve(Qfb(1, 1, 13), p))&&t[1]>=0, [1..1500]) \\ M. F. Hasler, Jan 15 2016

CROSSREFS

Sequence in context: A119869 A272200 A106904 * A098413 A174152 A103176

Adjacent sequences: A106900 A106901 A106902 * A106904 A106905 A106906

KEYWORD

nonn,easy

AUTHOR

T. D. Noe, May 09 2005

STATUS

approved