cp's OEIS Frontend

A084865 Primes of the form 2x^2 + 3y^2.

%I A084865 #27 Feb 09 2017 12:40:21
%S A084865 2,3,5,11,29,53,59,83,101,107,131,149,173,179,197,227,251,269,293,317,
%T A084865 347,389,419,443,461,467,491,509,557,563,587,653,659,677,683,701,773,
%U A084865 797,821,827,941,947,971,1013,1019,1061,1091,1109,1163,1181,1187
%N A084865 Primes of the form 2x^2 + 3y^2.
%C A084865 Subsequence of A084864; A084863(a(n))>0.
%C A084865 Conjecture: A084863(a(n))=1?
%C A084865 Is it true that a(n) = A019338(n+1)?
%C A084865 Comment: The truth of the conjecture A084863(a(n))=1 follows from the genus theory of quadratic forms (see Cox, page 61). By comparing enough terms, we see that the conjecture a(n) = A019338(n+1) is false. - _T. D. Noe_, May 02 2008
%C A084865 Appears to be the primes p such that (p mod 6)*(Fibonacci(p) mod 6)=25. - _Gary Detlefs_, May 26 2014
%D A084865 David A. Cox, Primes of the Form x^2 + n y^2, Wiley, 1989.
%H A084865 Vincenzo Librandi and Ray Chandler, <a href="/A084865/b084865.txt">Table of n, a(n) for n = 1..10000</a> [First 1000 terms from Vincenzo Librandi]
%H A084865 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 A084865 The primes are congruent to {2, 3, 5, 11} (mod 24). - _T. D. Noe_, May 02 2008
%e A084865 A000040(17) = 59 = 32 + 27 = 2*4^2 + 3*3^2, therefore 59 is a term.
%t A084865 QuadPrimes2[2, 0, 3, 10000] (* see A106856 *)
%o A084865 (PARI) list(lim)=my(v=List(),w,t); for(x=0, sqrtint(lim\2), w=2*x^2; for(y=0, sqrtint((lim-w)\3), if(isprime(t=w+3*y^2), listput(v,t)))); Set(v) \\ _Charles R Greathouse IV_, Feb 09 2017
%Y A084865 Cf. A084863, A084864, A019338, A084866, A139827.
%Y A084865 Primes in A002480.
%K A084865 nonn,easy
%O A084865 1,1
%A A084865 _Reinhard Zumkeller_, Jun 10 2003