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A283698 Numbers k such that {k^2 + 2, k^2 + 4} and {k^3 + 2, k^3 + 4} are twin prime pairs.

%I A283698 #22 Jan 10 2020 05:25:00
%S A283698 1,3,45,2055,39033,48585,101535,104553,112383,117723,129315,152553,
%T A283698 170793,178095,234483,246435,258093,272403,304845,306885,365343,
%U A283698 372663,375813,405393,405975,436425,456903,494193,538965,551475,559713,569805,570033,767895,792903
%N A283698 Numbers k such that {k^2 + 2, k^2 + 4} and {k^3 + 2, k^3 + 4} are twin prime pairs.
%C A283698 Except a(1), all terms are multiples of 3.
%C A283698 a(n) == {3 or 15} (mod 30) for n>2.
%H A283698 Amiram Eldar, <a href="/A283698/b283698.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..3665 from K. D. Bajpai)
%e A283698 a(2) = 3, {3^2 + 2 = 11, 3^2 + 4 = 13 } and {3^3 + 2 = 29, 3^3 + 4 = 31} are twin prime pairs.
%e A283698 a(3) = 45, {45^2 + 2 = 2027, 45^2 + 4 = 2029 } and {45^3 + 2 = 91127, 45^3 + 4 = 91129} are twin prime pairs.
%t A283698 Select[Range[1000000], PrimeQ[#^2 + 2] && PrimeQ[#^2 + 4] && PrimeQ[#^3 + 2] && PrimeQ[#^3 + 4] &]
%o A283698 (PARI) for(n=1, 100000, if(isprime(n^2+2) && isprime(n^2+4) && isprime(n^3+2) && isprime(n^3+4), print1(n, ", ")))
%Y A283698 Intersection of A086381 and A178337.
%Y A283698 Cf. A000040, A144953, A173255, A178336.
%K A283698 nonn
%O A283698 1,2
%A A283698 _K. D. Bajpai_, Mar 14 2017