login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Primes of the form 5x^2 + 21y^2.
1

%I #18 Sep 08 2022 08:45:33

%S 5,41,89,101,269,461,509,521,761,881,929,941,1049,1109,1181,1301,1361,

%T 1601,1721,1889,1949,2141,2309,2441,2609,2621,2729,2789,2861,3041,

%U 3209,3449,3461,3701,3821,3881,3989,4049,4241,4289,4409,4721,4889

%N Primes of the form 5x^2 + 21y^2.

%C Discriminant = -420. See A139827 for more information.

%H Vincenzo Librandi and Ray Chandler, <a href="/A139846/b139846.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 The primes are congruent to {5, 41, 89, 101, 209, 269, 341} (mod 420).

%t QuadPrimes2[5, 0, 21, 10000] (* see A106856 *)

%o (Magma) [ p: p in PrimesUpTo(6000) | p mod 420 in {5, 41, 89, 101, 209, 269, 341}]; // _Vincenzo Librandi_, Jul 29 2012

%o (PARI) list(lim)=my(v=List([5]), s=[41, 89, 101, 209, 269, 341]); forprime(p=41, lim, if(setsearch(s, p%420), listput(v, p))); Vec(v) \\ _Charles R Greathouse IV_, Feb 10 2017

%K nonn,easy

%O 1,1

%A _T. D. Noe_, May 02 2008