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A284058 Numbers k such that {k + 2, k + 4} and {k^3 + 2, k^3 + 4} are twin prime pairs.

%I A284058 #32 Jan 10 2020 05:25:43
%S A284058 1,3,69,1719,3555,8535,8625,9765,10065,17955,27939,32319,34209,35445,
%T A284058 39159,44769,47415,55329,56235,75615,85929,91965,96219,97545,98895,
%U A284058 122385,122595,138075,142695,143649,145719,152025,191829,192975,197955,200379,201819,202059
%N A284058 Numbers k such that {k + 2, k + 4} and {k^3 + 2, k^3 + 4} are twin prime pairs.
%C A284058 After a(1), all the terms are multiples of 3.
%C A284058 After a(2), all the terms are congruent to 5 or 9 (mod 10).
%C A284058 a(n) == {9 or 15} (mod 30) for n>2. - _Robert G. Wilson v_, Mar 19 2017
%H A284058 Amiram Eldar, <a href="/A284058/b284058.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..2352 from Robert G. Wilson v)
%e A284058 a(2) = 3, {3 + 2 = 5, 3 + 4 = 7} and {3^3 + 2 = 29, 3^3 + 4 = 31} are twin prime pairs.
%e A284058 a(3) = 69, {69 + 2 = 71, 69 + 4 = 73} and {69^3 + 2 = 328511, 69^3 + 4 = 328513} are twin prime pairs.
%t A284058 Select[Range[1000000], PrimeQ[# + 2] && PrimeQ[# + 4] && PrimeQ[#^3 + 2] && PrimeQ[#^3 + 4] &]
%o A284058 (PARI) for(n=1, 100000,2; if(isprime(n+2) && isprime(n+4) && isprime(n^3+2) && isprime(n^3+4), print1(n, ", ")))
%Y A284058 Intersection of A256388 and A178337.
%Y A284058 Cf. A000040, A001359, A086381, A144953, A178336.
%K A284058 nonn
%O A284058 1,2
%A A284058 _K. D. Bajpai_, Mar 19 2017