A033209 Primes of form x^2 + 11*y^2.

11, 47, 53, 103, 163, 199, 257, 269, 311, 397, 401, 419, 421, 499, 587, 599, 617, 683, 757, 773, 863, 883, 907, 911, 929, 991, 1021, 1087, 1109, 1123, 1181, 1237, 1291, 1307, 1367, 1433, 1439, 1543, 1567, 1571, 1609, 1621, 1697, 1699, 1753, 1873, 1907, 2003

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

Primes p such that the polynomial x^3-x^2-x-1 mod p has 3 zeros. Compare A106279. - T. D. Noe, May 02 2005

References

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

Links

• Vincenzo Librandi and Ray Chandler, Table of n, a(n) for n = 1..10000 (first 1000 terms from Vincenzo Librandi)
• Tim Evink, Paul Alexander Helminck, Tribonacci numbers and primes of the form p=x^2+11y^2, arXiv:1801.04605 [math.NT], 2018.
• N. J. A. Sloane et al., Binary Quadratic Forms and OEIS (Index to related sequences, programs, references)

Crossrefs

Primes in A243651.

Programs

Mathematica

QuadPrimes2[1, 0, 11, 10000] (* see A106856 *)

Extensions

Extended by T. D. Noe, Apr 17 2012