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A268475 Numbers n such that n^3 +/- 2 and 3*n +/- 2 are all prime.

%I A268475 #12 Sep 08 2022 08:46:15
%S A268475 435,555,2415,31635,38025,44835,80625,88335,97455,98505,99435,124335,
%T A268475 142065,145095,165375,176055,204765,246435,279225,293475,310095,
%U A268475 315555,332085,344745,348735,376935,392415,443595,462105,467385,482355,581415,609555,626775,636015
%N A268475 Numbers n such that n^3 +/- 2 and 3*n +/- 2 are all prime.
%C A268475 All the terms in this sequence are congruent to 0 (mod 5).
%C A268475 Each term in this sequence yields two sets of cousin prime pairs i.e., for n = 435 -> {82312877, 82312873} and {1307, 1303}.
%C A268475 All terms are congruent to 15 mod 30. - _Robert Israel_, Feb 05 2016
%H A268475 Robert Israel, <a href="/A268475/b268475.txt">Table of n, a(n) for n = 1..1000</a>
%e A268475 435 is in the sequence because 435^3 + - 2 =  82312877, 82312873; 3*435 + - 2 = 1307, 1303 are all prime.
%e A268475 555 is in the sequence because 555^3 + - 2 =  170953877, 170953873; 3*555 + - 2 = 1667, 1663 are all prime.
%p A268475 select(n -> andmap(isprime, [n^3 + 2, n^3 - 2, 3*n + 2, 3*n - 2]), [seq(p, p=1.. 10^6)]);
%t A268475 Select[Range[1000000], PrimeQ[#^3 + 2] && PrimeQ[#^3 - 2] && PrimeQ[3 # + 2] && PrimeQ[3 # - 2] &]
%o A268475 (PARI) for(n = 1,1e5, if( isprime(n^3 + 2) && isprime(n^3 - 2) && isprime(3*n + 2) && isprime(3*n - 2), print1(n ", ")))
%o A268475 (Magma) [n : n in [1..1e5] | IsPrime(n^3 + 2) and IsPrime(n^3 - 2) and IsPrime(3*n + 2) and IsPrime(3*n - 2)];
%Y A268475 Cf. A024893, A090121, A108701, A153183, A157834.
%K A268475 nonn
%O A268475 1,1
%A A268475 _K. D. Bajpai_, Feb 05 2016