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A084866 Primes that can be written in the form 2*p^2 + 3*q^2 with p and q prime.

%I A084866 #14 Dec 13 2021 08:04:32
%S A084866 83,173,197,269,317,389,461,557,653,701,797,941,1091,1109,1181,1229,
%T A084866 1637,1709,1949,1997,2069,2141,2309,2531,2549,2621,2789,2861,3221,
%U A084866 3389,3461,3581,3821,4157,4229,4349,4493,5051,5261,5381,5501,5693
%N A084866 Primes that can be written in the form 2*p^2 + 3*q^2 with p and q prime.
%C A084866 Subsequence of A084864 and of A084865; A084863(a(n))>0.
%H A084866 Robert Israel, <a href="/A084866/b084866.txt">Table of n, a(n) for n = 1..10000</a>
%e A084866 A000040(40) = 173 = 98 + 75 = 2*7^2 + 3*5^2 = 2*A000040(4)^2 + 3*A000040(3)^2, therefore 173 is a term.
%p A084866 N:= 10^4: # to get terms <= N
%p A084866 P:= select(isprime, [2,seq(i,i=3..floor((N/2)^(1/2)))]):
%p A084866 m:= nops(P):
%p A084866 R:= {}:
%p A084866 for p in P do
%p A084866   for i from 2 to m while 3*P[i]^2 <= N - 2*p^2 do
%p A084866     v:= 2*p^2 + 3*P[i]^2;
%p A084866     if isprime(v) then R:= R union {v} fi
%p A084866 od od:
%p A084866 sort(convert(R,list)); # _Robert Israel_, Nov 05 2020
%t A084866 nn = 10^4; (* to get terms <= nn *)
%t A084866 P = Select[Join[{2}, Range[3, Floor[Sqrt[nn/2]]]], PrimeQ];
%t A084866 m = Length[P];
%t A084866 R = {};
%t A084866 Do[For[i = 2, 3*P[[i]]^2 <= nn - 2*p^2, i++,
%t A084866      v = 2*p^2 + 3*P[[i]]^2;
%t A084866      If[PrimeQ[v], R = R ~Union~ {v}]],
%t A084866 {p, P}];
%t A084866 Sort[R] (* _Jean-François Alcover_, Dec 13 2021, after _Robert Israel_ *)
%Y A084866 Cf. A084863, A084864, A084865.
%K A084866 nonn
%O A084866 1,1
%A A084866 _Reinhard Zumkeller_, Jun 10 2003