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A254039 Primes p such that (p^3 + 2)/3, (p^5 + 2)/3 and (p^7 + 2)/3 are prime. 1

%I #17 Sep 08 2022 08:46:11

%S 524521,1090891,1383391,2633509,3371059,4872331,7304131,7756669,

%T 8819119,8877331,11536471,12290851,13362211,13509649,14658499,

%U 15359401,17094151,17582329,18191179,18550891,19416259,20465209,21971629,22519531,22619431,25972561,27155881,29281699

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

%C All the terms in this sequence are 1 mod 9.

%H K. D. Bajpai, <a href="/A254039/b254039.txt">Table of n, a(n) for n = 1..733</a>

%e a(1) = 524521;

%e (524521^3 + 2)/3 = 48102471044890921;

%e (524521^5 + 2)/3 = 13234061480615091039311002201;

%e (524521^7 + 2)/3 = 3640985160809159281478976663465873196681;

%e all four are prime.

%t Select[Prime[Range[10^7]], PrimeQ[(#^3 + 2)/3] && PrimeQ[(#^5 + 2)/3] && PrimeQ[(#^7 + 2)/3] &]

%o (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 (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 Cf. A241120, A253941, A253976, A253940.

%K nonn

%O 1,1

%A _K. D. Bajpai_, Jan 23 2015

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Last modified August 30 00:57 EDT 2024. Contains 375520 sequences. (Running on oeis4.)