A107152 Primes of the form x^2 + 45y^2.

61, 109, 181, 229, 241, 349, 409, 421, 541, 601, 661, 709, 769, 829, 1009, 1021, 1069, 1129, 1201, 1249, 1321, 1381, 1429, 1489, 1549, 1609, 1621, 1669, 1741, 1789, 1801, 1861, 2029, 2089, 2161, 2221, 2269, 2281, 2341, 2389, 2521, 2689, 2749, 3001, 3049, 3061, 3109, 3121, 3169, 3181

Offset

1,1

Comments

Discriminant = -180. See A107132 for more information.

Also primes of the form x^2 + 60y^2. See A140633. - T. D. Noe, May 19 2008

Also primes of the form x^2+6*x*y-6*y^2, of discriminant 60 (as well as of the form x^2+8*x*y+y^2). - Laura Caballero Fernandez, Lourdes Calvo Moguer, Maria Josefa Cano Marquez, Oscar Jesus Falcon Ganfornina and Sergio Garrido Morales (oscfalgan(AT)yahoo.es), Jun 24 2008

References

Z. I. Borevich and I. R. Shafarevich, Number Theory.

Links

Ray Chandler, Table of n, a(n) for n = 1..10000 [First 1000 terms from Vincenzo Librandi]

William C. Jagy and Irving Kaplansky, Positive definite binary quadratic forms that represent the same primes [Cached copy]

N. J. A. Sloane et al., Binary Quadratic Forms and OEIS: Index to related sequences, programs, references. OEIS wiki, June 2014.

D. B. Zagier, Zetafunktionen und quadratische Körper, Springer, 1981.

Formula

Primes congruent to {1, 49} (mod 60). - T. D. Noe, Apr 29 2008

Mathematica

QuadPrimes2[1, 0, 45, 10000] (* see A106856 *)
Select[Prime[Range[500]], MatchQ[Mod[#, 60], 1|49]&] (* Jean-François Alcover, Oct 28 2016 *)

Prog

(Magma) [ p: p in PrimesUpTo(3000) | p mod 60 in {1, 49 } ]; // Vincenzo Librandi, Jul 24 2012
(PARI) list(lim)=my(v=List(), t); forprime(p=61, lim, t=p%60; if(t==1||t==49, listput(v, p))); Vec(v) \\ Charles R Greathouse IV, Feb 09 2017

Crossrefs

Cf. A139643.

Cf. A141302, A141303, A141304 (d=60).

All representatives in A243188.

For a list of sequences giving numbers and/or primes represented by binary quadratic forms, see the "Binary Quadratic Forms and OEIS" link.

Sequence in context: A141919 A308797 A155571 * A141301 A139898 A171836

Adjacent sequences: A107149 A107150 A107151 * A107153 A107154 A107155

Keyword

nonn,easy

Author

T. D. Noe, May 13 2005

Status

approved