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A330438 Numbers k such that k^2-2 and k^3-2 are prime.

%I A330438 #15 Sep 08 2022 08:46:24
%S A330438 9,15,19,27,37,121,135,145,211,217,259,265,267,279,355,357,387,391,
%T A330438 435,489,525,561,615,621,727,951,987,1029,1119,1141,1177,1251,1287,
%U A330438 1357,1435,1491,1561,1617,1717,1785,1819,1839,1875,1909,1989,2001,2077,2107,2211
%N A330438 Numbers k such that k^2-2 and k^3-2 are prime.
%C A330438 Intersection of A028870 and A038599.
%H A330438 Robert Israel, <a href="/A330438/b330438.txt">Table of n, a(n) for n = 1..10000</a>
%e A330438 a(1) = 9: 9^2 - 2 = 79; 9^3 - 2 = 727; both results are prime.
%e A330438 a(2) = 15: 15^2 - 2 = 223; 15^3 - 2 = 3373; both results are prime.
%p A330438 filter:= k -> isprime(k^2-2) and isprime(k^3-2):
%p A330438 select(filter, [$2..10000]); # _Robert Israel_, Dec 24 2019
%t A330438 Select[Range[10000], PrimeQ[#^3 - 2] && PrimeQ[#^2 - 2] &]
%o A330438 (Magma) [n : n in [1 .. 100] | IsPrime (n^2 - 2) and IsPrime (n^3 - 2)];
%Y A330438 Cf. A028870, A028873, A038599, A038600, A108701.
%K A330438 nonn
%O A330438 1,1
%A A330438 _K. D. Bajpai_, Dec 14 2019