%I
%S 5,257,881,1013,1055,1133,1211,1475,1517,1715,1721,2771,2903,2981,
%T 3491,3821,4577,4661,4751,4907,5171,5795,6293,6347,6473,6557,6677,
%U 7481,7775,8393,8645,8951,9413,9701,9827,9905,10121,10241,10751,10883,10955,11045,11177
%N Integers n such that both 2*n^2 + 3*(n+2)^2 and 3*n^2 + 2*(n+2)^2 are prime.
%C Sequence is infinite assuming Schinzel's hypothesis H.  _Charles R Greathouse IV_, Dec 10 2012
%e 2*5^2+3*7^2 = 197 and 2*7^2+3*5^2 = 173 are prime.
%t Select[Range[20000], PrimeQ[2*#^2 + 3*(# + 2)^2] && PrimeQ[3*#^2 + 2*(# + 2)^2] &] (* _T. D. Noe_, Dec 10 2012 *)
%o (PARI) for(a=1,10000, c=a^2;b=(a+2)^2; if(isprime(2*c+3*b) && isprime(2*b+3*c), print1(a", ")))
%K nonn
%O 1,1
%A _Zak Seidov_, Dec 10 2012
