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A242244 Primes p such that both p^2 + 2 and p^2 - 2 are semiprimes.

%I A242244 #14 Apr 07 2018 10:32:21
%S A242244 11,17,53,73,79,83,97,251,269,281,379,389,433,461,601,631,691,739,827,
%T A242244 929,947,983,1033,1087,1187,1303,1423,1483,1531,1637,1709,1847,1879,
%U A242244 2447,2473,2683,2833,2843,3301,3463,3557,3719,3727,3779,3833,3907,3931,4157
%N A242244 Primes p such that both p^2 + 2 and p^2 - 2 are semiprimes.
%C A242244 Primes p such that p^2 + 2 = 3q, where q is prime, and p^2 - 2 is semiprime.
%H A242244 K. D. Bajpai, <a href="/A242244/b242244.txt">Table of n, a(n) for n = 1..3670</a>
%e A242244 a(1) = 11 is prime: 11^2 + 2 = 123 = 3 * 41 which is semiprime: 11^2 - 2 = 119 = 7 * 17 which is also semiprime.
%e A242244 a(2) = 17 is prime: 17^2 + 2 = 291 = 3 * 97 which is semiprime: 17^2 - 2 = 287 = 7 * 41 which is also semiprime.
%p A242244 with(numtheory):A242244:= proc()if isprime(x) and bigomega(x^2+2)=2 and bigomega(x^2-2)=2 then RETURN (x); fi; end: seq(A242244 (),x=1..5000);
%t A242244 A242244 = {}; Do[p = Prime[n]; If[PrimeOmega[p^2 + 2] == 2 && PrimeOmega[p^2 - 2] == 2, AppendTo[A242244, p]], {n, 2000}]; A242244
%t A242244 Select[Prime[Range[600]],PrimeOmega[#^2+{2,-2}]=={2,2}&] (* _Harvey P. Dale_, Apr 07 2018 *)
%o A242244 (PARI) is(n)=isprime(n) && isprime((n^2+2)\3) && bigomega(n^2-2)==2 \\ _Charles R Greathouse IV_, May 15 2014
%Y A242244 Cf. A000040, A005383, A063643, A115395.
%K A242244 nonn
%O A242244 1,1
%A A242244 _K. D. Bajpai_, May 09 2014