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%I #39 Sep 08 2022 08:45:18
%S 61,109,181,229,241,349,409,421,541,601,661,709,769,829,1009,1021,
%T 1069,1129,1201,1249,1321,1381,1429,1489,1549,1609,1621,1669,1741,
%U 1789,1801,1861,2029,2089,2161,2221,2269,2281,2341,2389,2521,2689,2749,3001,3049,3061,3109,3121,3169,3181
%N Primes of the form x^2 + 45y^2.
%C Discriminant = -180. See A107132 for more information.
%C Also primes of the form x^2 + 60y^2. See A140633. - _T. D. Noe_, May 19 2008
%C 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
%D Z. I. Borevich and I. R. Shafarevich, Number Theory.
%H Ray Chandler, <a href="/A107152/b107152.txt">Table of n, a(n) for n = 1..10000</a> [First 1000 terms from Vincenzo Librandi]
%H William C. Jagy and Irving Kaplansky, <a href="/A244019/a244019.pdf">Positive definite binary quadratic forms that represent the same primes</a> [Cached copy]
%H N. J. A. Sloane et al., <a href="https://oeis.org/wiki/Binary_Quadratic_Forms_and_OEIS">Binary Quadratic Forms and OEIS</a>: Index to related sequences, programs, references. OEIS wiki, June 2014.
%H D. B. Zagier, <a href="https://doi.org/10.1007/978-3-642-61829-1">Zetafunktionen und quadratische Körper</a>, Springer, 1981.
%F Primes congruent to {1, 49} (mod 60). - _T. D. Noe_, Apr 29 2008
%t QuadPrimes2[1, 0, 45, 10000] (* see A106856 *)
%t Select[Prime[Range[500]], MatchQ[Mod[#, 60], 1|49]&] (* _Jean-François Alcover_, Oct 28 2016 *)
%o (Magma) [ p: p in PrimesUpTo(3000) | p mod 60 in {1, 49 } ]; // _Vincenzo Librandi_, Jul 24 2012
%o (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
%Y Cf. A139643.
%Y Cf. A141302, A141303, A141304 (d=60).
%Y All representatives in A243188.
%Y For a list of sequences giving numbers and/or primes represented by binary quadratic forms, see the "Binary Quadratic Forms and OEIS" link.
%K nonn,easy
%O 1,1
%A _T. D. Noe_, May 13 2005
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