A033202 Primes of form x^2+93*y^2.

97, 109, 157, 193, 349, 373, 397, 421, 541, 577, 661, 733, 769, 853, 877, 937, 997, 1033, 1093, 1117, 1213, 1237, 1249, 1321, 1489, 1597, 1609, 1621, 1657, 1693, 1741, 1777, 1861, 1993, 2017, 2029, 2053, 2113, 2221, 2281, 2341, 2389, 2437, 2521, 2593, 2713, 2797, 2857, 2953

Offset

1,1

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]

N. J. A. Sloane et al., Binary Quadratic Forms and OEIS (Index to related sequences, programs, references)

Formula

The primes are congruent to {1, 25, 49, 97, 109, 121, 133, 157, 169, 193, 205, 253, 289, 349, 361} (mod 372). - T. D. Noe, Apr 29 2008

Mathematica

QuadPrimes2[1, 0, 93, 10000] (* see A106856 *)
Select[Prime@Range[500], MemberQ[{1, 25, 49, 97, 109, 121, 133, 157, 169, 193, 205, 253, 289, 349, 361}, Mod[#, 372]] &] (* Vincenzo Librandi, Jul 02 2016 *)

Prog

(Magma) [p: p in PrimesUpTo(3000) | p mod 372 in {1, 25, 49, 97, 109, 121, 133, 157, 169, 193, 205, 253, 289, 349, 361}]; // Vincenzo Librandi, Jul 02 2016
(Magma) [p: p in PrimesUpTo(3000) | NormEquation(93, p) eq true]; // Bruno Berselli, Jul 03 2016

Crossrefs

Cf. A139643.

Sequence in context: A346021 A232767 A039490 * A160032 A136477 A078494

Adjacent sequences: A033199 A033200 A033201 * A033203 A033204 A033205

Keyword

nonn,easy

Author

N. J. A. Sloane.

Status

approved