cp's OEIS Frontend

A254039 Primes p such that (p^3 + 2)/3, (p^5 + 2)/3 and (p^7 + 2)/3 are prime.

%I A254039 #17 Sep 08 2022 08:46:11
%S A254039 524521,1090891,1383391,2633509,3371059,4872331,7304131,7756669,
%T A254039 8819119,8877331,11536471,12290851,13362211,13509649,14658499,
%U A254039 15359401,17094151,17582329,18191179,18550891,19416259,20465209,21971629,22519531,22619431,25972561,27155881,29281699
%N A254039 Primes p such that (p^3 + 2)/3, (p^5 + 2)/3 and (p^7 + 2)/3 are prime.
%C A254039 All the terms in this sequence are 1 mod 9.
%H A254039 K. D. Bajpai, <a href="/A254039/b254039.txt">Table of n, a(n) for n = 1..733</a>
%e A254039 a(1) = 524521;
%e A254039 (524521^3 + 2)/3 = 48102471044890921;
%e A254039 (524521^5 + 2)/3 = 13234061480615091039311002201;
%e A254039 (524521^7 + 2)/3 = 3640985160809159281478976663465873196681;
%e A254039 all four are prime.
%t A254039 Select[Prime[Range[10^7]], PrimeQ[(#^3 + 2)/3] && PrimeQ[(#^5 + 2)/3] && PrimeQ[(#^7 + 2)/3] &]
%o A254039 (PARI) is(n)=n%9==1 && isprime(n) && isprime((n^3+2)/3) && isprime((n^5+2)/3) && isprime((n^7+2)/3) \\ _Charles R Greathouse IV_, Jan 23 2015
%o A254039 (Magma) [p: p in PrimesInInterval(3, 10000000) | IsPrime((p^3 + 2) div 3) and IsPrime((p^5 + 2) div 3) and IsPrime((p^7 + 2) div 3)]; // _Vincenzo Librandi_, Mar 27 2015
%Y A254039 Cf. A241120, A253941, A253976, A253940.
%K A254039 nonn
%O A254039 1,1
%A A254039 _K. D. Bajpai_, Jan 23 2015