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A106867
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Primes of the form 2*x^2+x*y+3*y^2, with x and y any integer.
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3
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2, 3, 13, 29, 31, 41, 47, 71, 73, 127, 131, 139, 151, 163, 179, 193, 197, 233, 239, 257, 269, 277, 311, 331, 349, 353, 397, 409, 439, 443, 461, 487, 491, 499, 509, 541, 547, 577, 587, 601, 647, 653, 673, 683, 739, 761, 811, 823, 857, 859, 863, 887, 929, 947
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OFFSET
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1,1
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COMMENTS
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Discriminant=-23. See A106856 for more information.
Primes p such that the polynomial x^3-x-1 is irreducible over Zp. The polynomial discriminant is also -23. - T. D. Noe, May 13 2005
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 1..1000
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MATHEMATICA
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Union[QuadPrimes[2, 1, 3, 10000], QuadPrimes[2, -1, 3, 10000]] (* see A106856 *)
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PROG
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(PARI) forprime(p=2, 10^4, if(0==#polrootsmod(x^3-x-1, p), print1(p, ", "))); /* Joerg Arndt, Jul 27 2011 */
(PARI) forprime(p=2, 10^4, if(polisirreducible(Mod(1, p)*(x^3-x-1)), print1(p, ", ") ) ); /* Joerg Arndt, Mar 30 2013 */
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CROSSREFS
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Cf. A086965 (number of distinct zeros of x^3-x-1 mod prime(n)).
Sequence in context: A105891 A141585 A191021 * A141861 A215379 A215375
Adjacent sequences: A106864 A106865 A106866 * A106868 A106869 A106870
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KEYWORD
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nonn,easy
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AUTHOR
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T. D. Noe, May 09 2005
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STATUS
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approved
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