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A107151 Primes of the form 5x^2 + 9y^2. 3

%I #20 Sep 08 2022 08:45:18

%S 5,29,41,89,101,149,269,281,389,401,449,461,509,521,569,641,701,761,

%T 809,821,881,929,941,1049,1061,1109,1181,1229,1289,1301,1361,1409,

%U 1481,1601,1709,1721,1889,1901,1949,2069,2081,2129,2141,2309,2381

%N Primes of the form 5x^2 + 9y^2.

%C Discriminant = -180. See A107132 for more information.

%C Except for 5, also primes of the form 9x^2 + 6xy + 26y^2. See A140633. - _T. D. Noe_, May 19 2008

%H Vincenzo Librandi and Ray Chandler, <a href="/A107151/b107151.txt">Table of n, a(n) for n = 1..10000</a> [First 1000 terms from Vincenzo Librandi]

%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)

%F Except for 5, the primes are congruent to {29, 41} (mod 60). - _T. D. Noe_, May 02 2008

%t QuadPrimes2[5, 0, 9, 10000] (* see A106856 *)

%o (Magma) [5] cat [ p: p in PrimesUpTo(3000) | p mod 60 in {29, 41 } ]; // _Vincenzo Librandi_, Jul 24 2012

%o (PARI) list(lim)=my(v=List([5]),t); forprime(p=29,lim, t=p%60; if(t==29||t==41, listput(v,p))); Vec(v) \\ _Charles R Greathouse IV_, Feb 09 2017

%Y Cf. A139827.

%K nonn,easy

%O 1,1

%A _T. D. Noe_, May 13 2005

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Last modified April 19 06:16 EDT 2024. Contains 371782 sequences. (Running on oeis4.)