cp's OEIS Frontend

A242326 Primes p for which p + 2, p^3 + 2 and p^5 + 2 are prime.

%I A242326 #44 Sep 25 2024 09:59:39
%S A242326 419,2339,14081,45821,46349,51419,56039,68489,70379,108191,112601,
%T A242326 115319,131891,132749,256391,267611,278879,314159,328511,342449,
%U A242326 361001,385139,424841,433259,470651,489689,519371,573761,664691,691181,694271
%N A242326 Primes p for which p + 2, p^3 + 2 and p^5 + 2 are prime.
%C A242326 Subsequence of A001359 and A048637.
%C A242326 All the terms in the sequence are congruent to 2 mod 3. This sequence is a subsequence of A240110.
%C A242326 Also, congruent to (11, 29) mod 30. - _Zak Seidov_, May 18 2014
%C A242326 Also, subsequence of A216976. - _Michel Marcus_, May 18 2014
%H A242326 Abhiram R Devesh, <a href="/A242326/b242326.txt">Table of n, a(n) for n = 1..1000</a>
%e A242326 419 is in the sequence because
%e A242326 p = 419 (prime),
%e A242326 p + 2 = 421 (prime),
%e A242326 p^3 + 2 = 73560061 (prime), and
%e A242326 p^5 + 2 = 12914277518101 (prime).
%t A242326 Select[Prime[Range[10^5]], PrimeQ[# + 2]&& PrimeQ[#^3 + 2]&& PrimeQ[#^5 + 2] &] (* _Vincenzo Librandi_, May 11 2014 *)
%o A242326 (Magma) [p: p in PrimesUpTo(10^6)| IsPrime(p+2) and IsPrime(p^3+2)and IsPrime(p^5+2)]; // _Vincenzo Librandi_, May 11 2014
%Y A242326 Cf. A001359, A048637.
%K A242326 nonn
%O A242326 1,1
%A A242326 _Abhiram R Devesh_, May 10 2014