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A107152
Primes of the form x^2 + 45y^2.
37
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
KEYWORD
nonn,easy
AUTHOR
T. D. Noe, May 13 2005
STATUS
approved