|
Search: id:A106867
|
|
|
| A106867 |
|
Primes of the form 2x^2+xy+3y^2, with x and y any integer. |
|
+0
3
|
|
| 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
(list; graph; listen)
|
|
|
OFFSET
|
1,1
|
|
|
COMMENT
|
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 (noe(AT)sspectra.com), May 13 2005
|
|
MATHEMATICA
|
f[x_, y_]:=2*x^2+x*y+3*y^2; lst={}; Do[Do[p=f[x, y]; If[PrimeQ[p], AppendTo[lst, p]], {y, -5!, 6!}], {x, -5!, 6!}]; Take[Union[lst], 5! ] [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Jul 04 2009]
Union[QuadPrimes[2, 1, 3, 10000], QuadPrimes[2, -1, 3, 10000]] (* see A106856 *)
|
|
CROSSREFS
|
Cf. A086965 (number of distinct zeros of x^3-x-1 mod prime(n)).
Sequence in context: A029737 A105891 A141585 this_sequence A141861 A092175 A072997
Adjacent sequences: A106864 A106865 A106866 this_sequence A106868 A106869 A106870
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
T. D. Noe (noe(AT)sspectra.com), May 09 2005
|
|
|
Search completed in 0.002 seconds
|
