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A155962 Numbers n with property that 3*(2n)^2+1 and 1*(2n)^2+3 are primes.

%I A155962 #7 May 30 2016 14:19:43
%S A155962 1,4,11,32,56,73,80,109,122,143,158,175,182,217,256,262,280,284,290,
%T A155962 308,343,347,403,431,434,437,535,581,598,619,655,665,928,973,980,1018,
%U A155962 1036,1046,1096,1120,1159,1207,1222,1235,1267,1382,1393,1439,1460,1463,1501
%N A155962 Numbers n with property that 3*(2n)^2+1 and 1*(2n)^2+3 are primes.
%C A155962 2*A155962 is intersection of A049422 and A111051.
%H A155962 Zak Seidov, <a href="/A155962/b155962.txt">Table of n,a (n) for n=1..1000</a>
%e A155962 n=1, {3*(2n)^2+1, 1*(2n)^2+3}={13,7};
%e A155962 n=4, {3*(2n)^2+1, 1*(2n)^2+3}={193,67};
%e A155962 n=11, {3*(2n)^2+1, 1*(2n)^2+3}={1453,487};
%e A155962 n=32, {3*(2n)^2+1,1*(2n)^2+3}={12289,4099}.
%e A155962 Resulting primes are congruent to 1 mod 3.
%t A155962 Select[Range[1600],AllTrue[{3(2#)^2+1,(2#)^2+3},PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* _Harvey P. Dale_, May 30 2016 *)
%Y A155962 Cf. A049422, A111051.
%K A155962 nonn
%O A155962 1,2
%A A155962 _Zak Seidov_, Jan 31 2009
%E A155962 All the terms in the b-file had to be divided by 2. Corrected by _N. J. A. Sloane_, Aug 31 2009.